You were comparing two things.
1) The roundness or flatness of the earth.
2) The rightness or wrongness of killing. — charleton

The reason I was comparing those two things is because people have been arguing that the killing is wrong as if it is objectively true yet that's what I have been refuting. I'm not the one saying 2 can be true like 1. I'm saying that has to be demonstrated, and that's what many people in this thread have been trying to do.

By 'they' I assume you mean definitions of morality in common usage? Haidt and Graham for example identify five common threads; Care, Fairness, Loyalty, Authority, and Sanctity, but others such a Bernard Gert list them as avoiding being the cause of death, pain, disability, loss of freedom, loss of pleasure, in that order (i.e, you might unavoidably be the cause of the later ones on the the list in order to avoid being the cause of the earlier ones). — Pseudonym

What is the reason for labeling this group of acts as morally right? Is the term morally right a label used for this group because it is a useful way to express the values of the majority of society (like care, fairness, etc.)? Meaning what is important and/or desirable to the majority of people in that society?

Murder is principally wrong because it goes against the nature of life itself. This can't be demonstrated as if it was a scientific fact, but can be demonstrated on other ways. Doesn't the fact that societies around the globe progressively traveled from allowing killing in many situations towards universal ban on killing tell you something? — Dalibor

All this tells me is that as societies have become more sophisticated, they have as a whole come to value not killing. This could be because attitudes have changed, because it is useful for cooperation purposes, safety, etc. Probably a combination of many reasons.

My main point is that when someone does something that others consider morally wrong, essentially what happened is that the person did something that goes against the values (what they find is important and/or desirable) of the majority in the absence of an objective morality. Until you can demonstrate some objective morality that goes beyond an expression of what the majority values, I have no reason to think that a murderer is doing anything other than being morally wrong in the sense that he is going against what the majority of people value, who have defined the term morality based off of that.

What is the reason for labeling this group of acts as morally right? — SonJnana

None. There's no more reason to the label than there is to the label "flat". You might as well ask "why do we group all things which are not curved or very bumpy together and call them all 'flat'?

What I've been trying to say right from the start is that there is a very important distinction between the identification of a set of similar behaviours (which is objectively verifiable) and the actions that one 'should' take as a result of such identification which are two separate things, in philosophy we call them Meta-Ethics and Normative Ethics respectively.

Yes, the reason why we've chosen those particular features to call 'good' and the opposite set to call 'bad' is to some extent an opinion, but it is no less an opinion than whether the earth is flat. 'Good' things all have similar traits, they seem to result in a particular type of human well-being (a long-term, stable sort of happiness). So to call the murder of innocents 'good' would be objectively wrong, it does not seem to result in any sort of long-term stable happiness like the other things in the group.

If I were to assert that grass was blue, you would have no trouble proving I was wrong, not because there is some universal dictionary written in the stars at the beginning of time to which we can refer. You would prove me wrong by lining up a whole load of things which are blue and noting that grass sticks out like a sore thumb.

It's no different with 'Good' and 'Bad'. You can line up all things already in the category 'Good' and see if your contested behaviour/thing fits with them or sticks out.

It's not your assertion that "murder of innocents is wrong" derives from the values of a particular society that I object to, It's your assertion that this is in some way categorically different from "the earth is flat", which, in exactly the same way, derives from a particular society's opinion about what 'flat' means. Neither come from some outside source, but neither are entirely subjective either, anyone trying to argue that a ball was flat could be countered by showing that a ball is unlike all the other things which we agree are flat; someone trying to argue that murder was good could be countered by showing how murder is unlike all the other things we call good.

It's not your assertion that "murder of innocents is wrong" derives from the values of a particular society that I object to, It's your assertion that this is in some way categorically different from "the earth is flat", which, in exactly the same way, derives from a particular society's opinion about what 'flat' means. Neither come from some outside source, but neither are entirely subjective either, anyone trying to argue that a ball was flat could be countered by showing that a ball is unlike all the other things which we agree are flat; someone trying to argue that murder was good could be countered by showing how murder is unlike all the other things we call good. — Pseudonym

The reason I was comparing flat and morally right is because flat is a word that describes a concept and unless you change the word, it will be true. As you've pointed out, that is what happens with morality as well and I don't disagree. Saying that something is morally right is dependent upon presupposed value and it's ambiguous. People have different values so people disagree on what is morally right. As as you acknowledged in a previous comment, what society as a whole considers morally right can change as values change. So what is morally right is subject to change depending on what people find important and/or desire, and practically there are a lot of differences between cultures and periods of time. I was just using that distinction to point out that people define what is morally right differently depending on their values and I don't see how there are "better" values, people just find different things important and therefore define morality differently. Though I think you made some good points and I don't disagree with what you've said.

It's not your assertion that "murder of innocents is wrong" derives from the values of a particular society that I object to — Pseudonym

When a person murders, what makes it wrong is that he committed an act in a group of acts that society has defined as morally wrong based off of society's values. I have no reason to think there is something "wrong" about it that goes beyond that. That's the main point of this thread and it seems as though you don't disagree, so I think we are on the same page unless I've misrepresented you.

The only point of disagreement that I'm sensing might still be there between our two positions is that the collection of acts must be coherent in themselves in order to justify a collective term 'moral acts'. It would be objectively wrong for such a collection of acts to be unconnected, even if that's what society wanted.

For example, let's say a particular culture decided it was immoral to wear a hat, walk upstairs two at a time, and eat fish. I would argue that such a society was objectively wrong for classifying those things as immoral even if every single member agreed on such a collection.

It defies meaning to say that an unconnected collection of objects/concepts all belong in the same group just because we say they do. That's just not how meaningful communication works.

So whilst it is society's values which define the requisite properties for items in the group, society owes its members a degree of consistency and coherence in their definition and I think it is objectively justified for anyone to call out inconsistency in this regard.

Murder is principally wrong because it goes against the nature of life itself. — Dalibor

"Life itself". Are you kidding?
Life and its evolution has always depended on killing as the ultimate act of competition which has given us the evolution of the most remarkable higher animals such as lions, tigers, killer whales and humans.

"Murder" is distinct from mere killing and is a legal, and therefore culturally specific, definition of a type of killing. Different cultures have different understandings of what killing is okay and what counts as murder, which is definitively "unlawful killing". Since law is not natural but a cultural artefact it cannot be said to be related to the "nature" of life in any sense.

Society can decide whatever they want to be morally right. The acts have to be similar by being consistent with the presupposed values that society has decided upon, or else the acts by society’s own definition wouldn’t fit the term morally right. So i think we are in agreement here as well.

Excellent! Which means it is not morally wrong if I treat your statement as if it is morally wrong. The problem is, your statement cannot support itself with its own claims.

If all claims are equally valid, then all claims are also equally invalid, including yours. At that point, its just whoever desires something more strongly and capably, which is more about power than the concept of morality.

of course, you could argue that power is morality, depending on how you define it. Foucault's truth/power hybrid , inspired by Nietzsche, defines truth in terms of values, and values in terms of power , and power as something that flows through and creates individual subjectivity but isn't controlled by individuals.
If you think this is an unsatisfactory account, the challenge is to transcend it without falling back on a realist view of morality.