I am an atheist and I might be wrong, those aren't mutually exclusive.

Every person who actively holds the belief that there is a god is theist. EVERY other person is an atheist. Whether that's people who lack that belief, or people who believe the opposite, or even people who have no concept of the concept of a god, all "atheist"

If I don't know whether or not there is a god, that makes me an atheist, because I'm a-theist, not-theist.

Agnostic on its own does not make sense, it's not a third category. That's because "theist" means "belief in a god or gods", not "belief in a god or gods, AND knowing it is correct."

Someone can not believe the claim, but also not believe the opposite claim.

I am an atheist and I might be wrong, those aren't mutually exclusive.

Every person who actively holds the belief that there is a god is theist. EVERY other person is an atheist. Whether that's people who lack that belief, or people who believe the opposite, all "atheist"

If I don't know whether or not there is a god, that makes me an atheist, because I'm a-theist, not-theist.

Agnostic on its own does not make sense, it's not a third category. That's because "theist" means "belief in a god or gods", not "belief in a god or gods, AND knowing it is correct."

Someone can not believe the claim, but also not believe the opposite claim.