That this proof is still of such high interest can be seen in a critical video of the atheist Youtuber Rationality Rules with the title:

Ben Shapiro calmly EDUCATED by Stephen Woodford

After all, Rationality Rules`s video is his second most viewed video with over 770000 clicks.

In the video description, he lets the following be known, among other things:

"As always, thank you kindly for the view, and I hope that this video explains just some of the major issues with Aristotle / Aquinas / Shapiro / Feser’s unmoved mover / unactualised actualiser."

Only I found that his video is not so strong from a philosophical perspective. That is why I have taken the great trouble to do a critique of the proof in its popularly presented form myself on the basis of the relevant literature. Even though it has become very long, I think it is worth reading if you are interested in such things. I start with a summary of the proof. The summary refers to the full argument of the currently most famous Thomism popularizer Edward Feser in his book "The Last Superstition". I may be rightly accused of not doing justice to Feser, but I think the summary gets to the heart of the basic idea, and this is how the proof is mostly presented orally. The rest explains itself, if one reads the critical quotations.

Here is the summary of the alleged proof:

"In Chapter 3 Feser discusses three of St. Thomas's magnificent five ways, describing the first way with customary clarity and succinctness. Noting that "no potential can make itself actual" (p. 91), Feser points to St. Thomas's well known example of a man pushing a stone with a stick. The stone's potency to move is actualized by the stick, whose potency to move is actualized by the hand, whose potency to move is in turn actualized by the firing of certain motor neurons, and so forth. In this, an essentially subordinated series, each actualized potency is simultaneously actualized by a superior. Feser notes that such a series "of its nature, must have a first member" because "it is only the first member which is in the strictest sense really doing or actualizing anything" (p. 95). Without a first Pure Act [God] free from all admixture of potency, there are no other actualities, nor can there be, since all others "exist at all only insofar as yet earlier ones do" (p. 95)." (an official review by Michael O'Halloran)

By "and so forth" Feser means the existence of molecules, atoms and quarks and whatever else may be smaller. Aquinas would add:

"this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover, seeing that subsequent movers move only inasmuch as they are moved by the first mover."

And he concludes:

"Therefore it is necessary to arrive at a first mover, moved by no other; and this everyone understands to be God."

However, one does not arrive at an in every respect actual unmoved mover:

"Assuming that Aquinas can block a regress in the case of movers and things moved, why must the primary mover be not just unmoved, but unmovable? Aquinas thinks that if the mover of some moved thing is not itself moved, it is an unmovable mover [...]. What justification does he have for supposing that an unmoved mover is unmovable? The sort of causal series he has in mind in the proof from motion has as a member something, M, that is being moved. M’s going from being in potentiality with respect to some state S to being in actuality with respect to S needs to be explained by some primary mover, P. All that is required of P is that it be in actuality with respect to S; P’s being in actuality with respect to S is what makes P the primary mover in this causal series ordered per se. So in order to count as a primary mover, as the stopping point in a causal series ordered per se, P must be unmoved (because it is in actuality) in the relevant respect. But it does not follow from this that P must be unmoved (and hence in actuality) in all respects. If P were in actuality in all respects, P would be absolutely unmoved and unmovable, but the fact that P is unmoved with respect to some state S does not entail that P is unmovable. Given that Aquinas’s argument so far has shown only that there must be some primary mover that is in actuality in the respect relevant to the particular case of motion at hand, it seems likely that there will be very many relatively uninteresting primary movers. The fire in our paradigm case seems to be a suitable primary mover, animals (or their souls) might be unmoved movers, and some of Aquinas’s own examples of causal series ordered per se apparently have human beings filling the role of primary mover, at least as Aquinas describes them. We might call fire, animals, human beings, and other natural unmoved movers (if there are any) mundane primary movers. The problem, then, is that the proof from motion gives us no reason to suppose there are any primary movers other than mundane primary movers." (Scott Macdonald - Aquinas’s Parasitic Cosmological Argument)

Mundane primary movers may result from accidentally ordered series (non-instrumental, non-simultaneous):

"An alternative strategy is to argue that every essentially ordered causal series has a first member, where a causal series is essentially ordered if no effects within the series can exist without their causes also existing (e.g., the movement of a stone depending upon the pressure of a stick). The thought is that even if some causal series can be infinite, no essentially ordered can be. A proponent of this strategy faces the challenge of explaining why a first cause in an essentially ordered series could not have been caused by things within a non-essentially ordered causal series." (Joshua Rasmussen - Cosmological Arguments from Contingency)

Aristotle himself gives an example for an accidentally (non-essentially) ordered causal series:

"As, when something has caused motion in water or air, this moves another and, though the cause has ceased to operate, such motion propagates itself to a certain point, though there the prime mover is not present[.] [464a1] [5]" (ARISTOTLE - ON DIVINATION IN SLEEP)

[edit: Here is an alternative translation:

"When something has moved a portion of water or air, and this in turn has moved another, then even when the initial impulse has ceased, it results in a similar sort of movement continuing up to a certain point, although the original mover is not present." (Filip Radovic - Aristotle on Prevision through Dreams)]

In such an order, not all members need to coexist (e.g. father and son).

Feser's example of the proof of God originally comes from Aristotle:

"The example [Aristotle] most often gives—a man using his hands to push a spade to turn a stone—suggests a series of simultaneous movers and moved. We may agree that there must be a first term of any such series if motion is ever to take place: but it is hard to see why this should lead us to a single cosmic unmoved mover, rather than to a multitude of human shakers and movers. […] Aristotle himself at one point seems to agree with this objection, and to treat a human digger as a self-mover (256a8)[:]" (Anthony Kenny – A New History of Western Philosophy)

"e.g. the stick moves the stone and is moved by the hand, which again is moved by the man; in the man, however, we have reached a mover that is not so in virtue of being moved by something else." (Aristotle – Physics)

Elsewhere Aristotle wants to rule out self-movers:

"The basic principle of Aristotle’s argument is that everything that is in motion is moved by something else. At the beginning of book 7 of the Physics he presents a reductio ad absurdum of the idea of self-movement. A selfmoving object must (a) have parts, in order to be in motion at all; (b) be in motion as a whole, and not just in one of its parts; and (c) originate its own motion. But this is impossible. From (b) it follows that if any part of the body is at rest, the whole of it is at rest. But if the whole body’s being at rest depends upon a part’s being at rest, then the motion of the whole body depends upon the motion of the part; and thus it does not originate its own motion. So that which was supposed to be moved by itself is not moved by itself [...]. This argument contains two fallacies." (Anthony Kenny – A New History of Western Philosophy)

These are the fallacies:

"First, it equivocates between logical and causal dependence, as Sir David Ross points out in his commentary on Physics 242a 38: ‘the motion of the whole logically implies the motion of the part, but is not necessarily causally dependent on it’. (Ross, p. 669). Secondly, it equivocates between being a necessary condition and being a sufficient condition. The part’s being at rest is a sufficient condition for the whole’s being at rest; from this it follows only that the motion of the part is a necessary condition for the motion of the whole, and not that it is a sufficient condition for it. Hence the argument in no way proves that something else, namely the motion of the part, is a causally sufficient condition for the motion of the alleged self-mover. So the reductio ad absurdum fails: it has not been shown that there cannot be a body which can initiate its own movement without external causal concurrence." (Kenny, Anthony - Five Ways)

Self-motion could be explained in the following way:

"In fact, the First Way cannot deny that there are non-processes that are active, because it argues to one. But in point of fact, both Aristotle and St. Thomas held that there are acts that seem to be processes and are not, and yet are not the First Mover. These are transitions of a sort, but not transitions from potency to act. The most common example they give of such a transition is that of not seeing to seeing. […] This type of pseudo-process, then, is a transition from act to act, and the being does not acquire something that it does not already have. Another example would be actively thinking about some fact that one already knows, but was not thinking of before. One is no greater for thinking about it, because one already knows it. One could say that there is a change in some sense going on here, but it is a peculiar one, one that could be called, in modern terms, a change of phase rather than a change of state. Now such transitions are most obvious in the operations of living things, but are not confined to them. […] And this leads us back to the First Way in the light of St. Thomas’ own philosophy. Since he admits, as was said earlier, that there are transitions that are not processes, then all the First Way really argues to in Thomism is to a living being, which is defined as one which can set up its own process. (Summa Contra Gentiles, IV, c. 20.) Of course, the living being does not "move itself" (movere se) in the respect in which it is in process, but processes like growth or movement of the limbs are initiated from the soul, or the “first act” within the being, and so have as their cause one of those transitions from act to act." (George A. Blair – Another Look at St. Thomas' "First Way")

Here is a suggestion that the mind moves the body:

"The [mind] is an entity and yet not a “res . . . ,” because it is the complete dynamism of [a] substrate-less absolute change [keyword: stream of consciousness as inner motion].“ […] As an entity of time [the mind or subject] would then be precisely the form of motion of a body. For as the subject in a form of one, namely, its own body, the subject would be exactly that which through itself as that completely special type of constant motion would place its body in motion or at rest: already as a cognizing, and thus first and truly as an acting subject." (Gerold Prauss - The Problem of Time in Kant)

The mind would appear on the basis of a highly complex organized body. One would also have to say that it would emerge from the body in an entirely natural way.

Natural motions, according to current theoretical physics, generally do not require continuous causation:

"Most important for our purposes, the whole structure of Aristotle’s argument for an unmoved mover rests on his idea that motions require causes. Once we know about conservation of momentum, that idea loses its steam. [...] There is conservation of momentum: the universe doesn’t need a mover; constant motion is natural and expected. [...] The universe doesn’t need a push; it can just keep going." (Carroll, Sean - The big picture)

There are philosophical explanations for this:

"Some Thomists claim that the crucial fact which the First Way seeks to explain is not the tendency which a heavy body has to fall — this, they admit, is something which was given to the heavy body by whatever it was in the past which made it heavy — but rather the current exercise of that tendency in actual motion. Every such potentiality of a creature, they say, needs to be actualized by the immediate action of the Creator. This seems to be a piece of nonsense. To say that something has a tendency to move is precisely to say that unless something interferes, it will move; if it moves therefore, when interference is removed, no further explanation of its motion is called for apart from the tendency and the removal of the interference." (Kenny, Anthony - Five Ways)

And:

"But it seems that at least things in perpetual motion could be self-movers. It seems, in Aquinas’s Aristotelian terms, that they could be at every moment things actually in motion and potentially in motion in the immediate future, their changing potentialities being continuously actualized by the action of their immediately antecedent actualities." (Jordan Howard Sobel - Logic and Theism Arguments: For and Against Beliefs in God)

The effect of gravity ends with large masses, which themselves would be nothing but mundane primary movers:

"But to someone outside the solar system, they would not see a force at all; they would observe that the space around the Earth has curved, so that empty space is pushing the Earth so that it goes in a circle around the sun. Einstein had the brilliant observation that gravitational attraction was actually an illusion. Objects moved not because they are pulled by gravity or the centrifugal force but because they are pushed by the curvature of space around it. That’s worth repeating: gravity does not pull; space pushes. […] For example, you might be sitting in a chair right now, reading this book. Normally, you would say that gravity is pulling you down into your chair, and that is why you don’t fly off into space. But Einstein would say that you are sitting in your chair because the Earth’s mass warps the space above your head, and this warping pushes you into your chair. [...] Now replace the marble with the Earth, the shot put with the sun, and the mattress with space-time. [...] This is the insight of what Einstein called general relativity: space-time is warped by heavy masses, causing the illusion of gravitational force." (Kaku, Michio. The God Equation)

Thus, large masses move (curve) the space and the space moves smaller masses in the direction of the larger masses.

One could identify two kinds of potential in Aristotle:

"My proposed interpretation will be based upon introducing [a] double feature of potentiality as a basic tenet of Aristotle's physics. I'll argue that there are two distinct kinds of potentials, the one consisting of potentials that are marked by their being logically entailed by the given existence of the actual, and the other, of potentials that are merely suggested by similarity or inductive considerations. The ontological difference between them is that whereas the entailed potential is fully effectual [...], the analogical or inductive potential is merely a necessary condition and thus necessarily ineffectual. [...] I'll use the terms "genuine" and "nongenuine" respectively to refer to these two modes of potentiality." (Zev Bechler - Aristotle's Theory of Actuality)

Nongenuine potentials

"are nonreal things." (Zev Bechler)

Genuine potentials, on the other hand,

"can be movers[.]" (Bechler)

This follows from all:

"[T]he proof of the necessity of a first unmoved mover is destroyed: No such mover is needed, nor de facto exists in the natural motion of the elements, where only the genuine potential is the mover. Hence the cosmic chain of mover-moved breaks down at each case of continuous natural motion, that is, of both living things and the five elements." (Bechler)

In the face of all these counterarguments, Feser turns the First Way into a composition argument as a way to save it. However, Feser is not the first to do so:

"In an attempt to vindicate the celebrated "Five Ways," John Lamont tries to show that Aquinas's arguments for an uncaused cause are successful provided they are understood as resting on an argument from composition.' Lamont further seeks to show that an uncaused cause must be immaterial and unique. In this paper, however, I shall argue that even if we accept the translation of Thomas's various proofs into an argument from composition, such an argument need in no way be thought of as implying the existence of an uncaused cause. Further, I shall show that Lamont's argument for the immateriality of the uncaused cause is problematic and his argument for its uniqueness unconvincing. [...] To sum up: Lamont, following Peter Geach, tries to show that Aquinas's proofs for the existence of God can be construed as a valid composition argument. I have argued that insofar as we can reduce the Five Ways to a composition argument, such an argument in no way yields the desired conclusion. The failure of Lamont's attempt is explained by the fact that he makes the proof of God's existence into a deductively valid composition argument only by begging the question with respect to the fundamental issue, namely, that the sum of all effects is really a group in need of a singular cause different from the causes of any of the effects of which it is the aggregate. Finally, inspection of Lamont's reasons for arguing in favor of God's immateriality and uniqueness reveals that such attributes could be seen to be validly predicated of God only by excluding alternative hypotheses which Lamont does not even envisage." (ANTOINE COTE - THE FIVE WAYS AND THE ARGUMENT FROM COMPOSITION)

The big problem is that Feser basically does not believe in the ontologically prior efficacy of parts at all:

"For example, if a stone is a true substance, then while the innumerable atoms that make it up are real, they exist within it virtually or potentially rather than actually. What actually exists is just the one thing, the stone itself." (Edward Feser – Aristotle's Revenge)

To this must be added the following:

"Since (per one of Feser’s premises) only actual things can actualize something’s potential for existence, it follows that the parts Feser adduces cannot causally actualize the existence of the substances they compose." (Joseph C. Schmid - Existential inertia and the Aristotelian proof)

Hence, Feser thinks holistically, and that amounts to:

"According to holism, the table in front of you does not derive its existence from the sub-atomic particles that compose it; rather, those sub-atomic particles derive their existence from the table." (Philip Goff - Is the Universe a conscious mind?)

This means that parts cannot cause the whole, which is contrary to the point the composition argument is trying to make.

Here, the holism of an animal is presented taking a leopard as an example:

"A leopard is self-moving because the action of one part of it, the brain, which is an action of the leopard, moves another part of it, the legs, which is a movement of the leopard. […] I mean we think of the leopard as the natural unit of which the legs and brain are essentially parts; being a part-of-the-leopard is what it is for the leg to be what it is; it has its existence as what it now is by being a part of the leopard. The whole leopard, so to say, comes first. The parts are secondary. If the leg ceases to be part of the leopard it will turn into something completely different, as mutton is something completely different from a sheep. So a leopard is alive because it has organs which exist as what they are precisely by being organs, being functioning parts of a prior whole." (Herbert McCabe - On Aquinas)

Intuitively, one rightly assumes that once holistic things begin to exist, they will persist for some time:

"I say that [a] chair’s existence at t + ε is fully explained by the actualization of the potential, possessed by the chair at t, to continue to exist through t + ε, and the absence of anything that intervenes to prevent the realization of this potential." (GRAHAM OPPY - On stage one of Feser’s ‘Aristotelian proof’)

One can add that

"most things naturally tend to remain in existence." (Anthony Kenny - Medieval Philosophy)

Feser is at least a reductionist in his God-proof reconstruction and therefore must assume simples that God generates and moves so that they can move everything else in the world. If the transcendent God is the first member of the causal series, then something physically indivisible must stand in the second place (but in the first place within the immanence), because otherwise it would not be at exactly that second position. Doesn't God then seem completely superfluous and can't we save ourselves the incredible leap to the transcendent?

For to

"[j]ump from a first immanent cause to a first transcendent cause appears [it doesn't only appear so] to be one of the most questionable moves in the Thomistic program." (Edward N. Martin – Infinite Causal Regress and the Secunda Via)

Yet even more baffling, Feser

"offers us the explanation that God is the first transcendent cause, which, given God’s eternality and immutability, is prima facie [but not only prima facie] very hard to accept." (Edward N. Martin)

Immanent (fundamental) particles would thus suffice to explain everything under the plausible assumption of naturalism. If one sees a barely surmountable difficulty regarding the hard problem of consciousness, then naturalistic panpsychism (Philip Goff) or naturalistic dualism (David Chalmers) could be helpful additional presuppositions.

A further remark shall be made here to the particles which would be indivisible atoms of matter without further substructure, having absolute cohesion of their homogeneous minimum extension, which could only be misunderstood by mathematical minds as a sum of discrete parts:

"[E]ven though [they] have spatial extent, the question of their composition is without any content." (Brian Greene - The Elegant Universe)

Aquinas also seems to agree with this in some way:

"For example, in his commentary on Aristotle's Physics, Aquinas writes of natural minima that, “although a body, considered mathematically, is divisible to infinity, the natural body is not divisible to infinity.”" (wikipedia on Minima naturalia)

One can also grant the Thomists a certain version of a hylemorphism, if it absolutely must be.

It would be a concrete, naturalistic hylemorphism. Form and matter of a particle would not be like two heterogeneous, abstract things, which would have to be put together awkwardly by a god. There would be a natural duality of two aspects, form and matter, within the absolute unity of the particle. The aspects would be in a certain sense consubstantial or nature-like, whereby the matter would be something like dammed up, potential energy of a rest mass and the form would be something like like an electromagnetic field energy, which arises from the matter, constantly originates and passes away and therefore can "move" the matter smoothly and continuously and produce complex stuff.

Here is a similar description:

"The form, or nature, or essence, is some definite component sitting inside the matter but distinct from it in a simple, physical sense, like the balloon from the helium it contains. [...] Aristotle's forms are not parts or components within the object because, being aspects, they are not the kind of thing that can compose their object." (Zev Bechler - Aristotle's Theory of Actuality)

Form and matter would necessarily always go hand in hand, and they would have always existed and will do so in all eternity, always making up the indissoluble unity of a particle, all without energy loss. Nothing supernatural at play. And perhaps only in our mind, that is, only conceptually, the particle has a dual aspect nature, but extramentally, that is, in reality, it is probably one in a strict sense.

The attempt to save Aquinas' proof by making it a composition argument fails. The supposed saviors want to say: parts compose (move) the whole and these parts are composed by further parts and this cannot go to infinity. I say that this is refuted by holistic wholes or fundamental particles.