Actually, all I've done is ask atheists to share their logical reasoning as I have done.
You also insisted atheism is a belief or claim, or involves a belief or claim, which it need not. Since atheism is defined as the lack or absence of belief in any deity or deities. Logically a claim or belief is is not proved because it cannot be disproved, and vice versa, this is called an argumentum ad ignorantiam fallacy.
I can only offer my own position, which is that I don't believe in any deity or deities, for the same reason I disbelieve anything, that no objective evidence can be demonstrated for it.
God concepts can be split into falsifiable and unfalsifiable claims, we can know nothing about unfalsifiable claims, thus I would also have to be agnostic about those.
I am therefore an atheist, and an agnostic where the deity being premised is an unfalsifiable concept, this seems logically consistent to me.
just have to give us some idea of what atheism's functional value, is.
Why must it have a functional value? Does your disbelief in say invisible mermaids have a functional value? You can replace that with a falsifiable concept if you prefer, but nothing that simply feeds into your belief in a deity as that strikes me as a circular reasoning fallacy, but if you think otherwise present it and I will see.