Water,water said:How does it have nothing to do with identity?
Why define yourself as a-something -- unless this something has an important bearing on that identity of yours?
I could call myself a, say, "afetishist" -- but that would make sense only in regards to fetishism.
Ex negativo definitions are not very useful, and tend to be misleading. I think a new, ex positivo definition and name for at least some of those that now consider themselves "atheists" is needed.
On second thought, I suppose it's possible for some to define themselves in opposition to theism. I don't think it is a necessary attribute of atheism, though. It could be that atheism was created by religious people to define themselves. Isn't the bible full of declarations of hethenism and paganism? The people they describe might not agree, and counter that they are very religious, just not in a monotheistic way. Buddhists, for example, fit the dictionary definition of atheists, but don't define themselves that way. There are some religions that fall in the middle. Some Native American religions are monotheistic, but their God is not the Christian God, so what are they?