When we are discussing the existence of God, there are three main positions:

Theist: I believe God exists.
Atheist: I believe God does not exist.
Agnostic: I neither believe God exists nor that God does not exist.

This is just like any other normal ontological issue, such as the existence of universals, objective morality, other minds, etc.

Unfortunately these terms are abused a lot, which obfuscates things. There are the colloquial terms "agnostic (a)theist" which, to my understanding, seek to describe a position in which a person is not totally sure if God does or does not exist but believes in (a)theism anyway. This is awfully frustrating because it 1.) begs the question and 2.) removes real agnosticism as a legitimate position.

For most self-professed agnostic atheists, it is the theists who hold all the burden of proof. In the absence of evidence, it can be assumed God does not exist, or so the agnostic atheist claims. Usually this is accompanied by some pseudological "you can't prove a negative".

Firstly, you can prove a negative and we do it all the time. If we mean logical proof, we need only show a logical error that invalidates something's existence, such as a married bachelor. If we mean through induction, we need depend on the same criteria of evidence that would be used for a positive claim. We might say, there is no elephant in the room, and then turn on the lights and say look! there's no elephant!

It is question-begging to assume atheism is the "null" position as agnostic atheists are so inclined to believe, because it ignores the fact that we need to have a reason why atheism would be the null position, which would simply be an argument for atheism. This argument may simply be the acceptance of naturalism or physicalism. But oftentimes it is accompanied with positive skeptical arguments, such as the relativity of religion, or the evil in the world, or whatever.

Ultimately then, there are no null-positions in philosophy. There are only more deeply-held beliefs. Atheists as much as theists need to provide reasons for why they believe what they believe. An argument for atheism is not that theism has failed to give good arguments, but that this failure constitutes a reason to reject theism because of some prior held commitment (such as naturalism or whatever).

What interests me, though, is why people feel the need to "qualify" their (a)theism in this way. And I think it's because the question of God's existence is not simply an academic one but one that affects the very core of our worldviews. How we orient ourselves to the world is influenced by our perspective on God's existence. It's not like, say, the existence of a planet with purple oceans. How would the existence of such a planet really affect our ways of living?

So I think people are "paralyzed" by agnosticism. They don't know how to live life as an agnostic. Agnostic atheists in my experience have often claimed that atheists and agnostics "live the same", in the sense that they live without a belief in God. The problem here is that if you live "as if" God does not exist, then you seem to have already made a commitment - atheism. In this case it seems that atheism must be a pragmatic position to hold - we don't have all day to think about God's existence.

(On the pragmatic level, then, the question of God would seem to be more about the question of a certain kind of God: a loving, personal, immanent, miracle-worker. I think most agnostic atheists will say they not only lack belief in this God but also believe he does not exist. What they may still be unsure about is the clockwork, deistic God, or perhaps the more technical philosophical God. In that sense they may be agnostics.)

Now the question I'm interested in is how the agnostic and atheist "lifestyle" are different. And I think a plausible answer (at least in part) is that we can separate the theoretical from the pragmatic/emotional. Theoretically I am an agnostic - I realize there are good arguments for, and serious objections to, both theism and atheism. But on the pragmatic/emotional level, I orient myself in life as though God does not exist. I don't expect miracles, I don't expect to go to the afterlife after I die, I don't pray or worship or any of that. All of this is consistent to what an atheist would (not) do.

The crucial part of this, from my own self-analysis, is that although this pragmatic assumption that God does not exist may have some loose reasons backing it up, a lot of it strikingly has to do with feelings, values and desires. I don't like the idea of God being real! I don't like the idea of an all-powerful, all-knowing entity that I cannot escape from! I like the world in which a God does not exist more than the world in which he does. I don't like organized religions and the influence they have on politics and psyches. I want to be free, independent, and self-sufficient.

Yet it could also be said that perhaps morality is dependent on God's existence. An theoretical agnostic might feel compelled to believe in God for the sake of morality. Or due to Pascal's wager. I'll copy part of a summary of Levinas' Jewish thought that I wrote elsewhere:

"Monotheistic alterity is the religious belief of the adult, but can only come at the risk of atheism. Ontology is atheism; negative theology is unacceptably positive. Religious ecstasy is a violence against human freedom, which is itself born from the breaking of the core of consciousness by the trace of the transcendent (Ileity). Devotion requires responsibility: social justice is the means in which humans attain redemption; it is a pre-eminently religious act."

Levinas was Jewish, and (I think?) he was a theist, but not in the sense of there being a God within the totality but as alterity; we know of God only by his "trace", i.e. his absence shows his presence. Levinas' God does not fit the role in the traditional sense. He calls for an adult religion of responsible and independent thinking followers. This makes his form of theism difficult to differentiate from atheism in terms of "lifestyle".

Thus I conclude that in many cases, "agnostic atheism" is actually just veiled anti-theism. It is hatred of God even if he doesn't exist. The idea that agnostics and atheists act "the same" is false, since an agnostic may also act "the same" as a theist. The "agnostic atheist" is someone who knows there may be arguments for theism but have failed to read them and have decided to reject theism anyway. That's the only explanation I can see, since they beg the question by asserting "agnostic atheism" is the "null" position.