Atheism is not limited to "believing there are no deities." People have been conditioned to think--with this limited definition--that atheism and theism somehow cover all aspects of belief/no belief. Atheism isn't limited to denial. Theism is belief, atheism is no belief.

Atheism means "not believing in the existence of a supreme being." While this difference seems subtle, it is very disparate. A person born on an island and raised by wolves may not even know about deities. He has no belief in what he doesn't know to believe or deny. He is an atheist. A child who has not learned about people's beliefs in a god cannot believe. The child is an atheist. There is no belief in a deity, which is atheism.

They are not two sides of the same coin. Atheism isn't even a belief! With unicorns, vampires, "unigoates" (I made this one up), or the Flying Spaghetti Monster, not believing in them doesn't mean you have a belief! If it's no belief, it can't be an idea.

Atheism isn't "knowing about people's religions, superstitions, or faith in a god and then denying it for various reasons." It is simply "no belief" in a god, supreme being, deity, supernatural force, etc. Even if you state "I am sure there is no god" this is still "no belief" in a god.

Agnosticism isn't a different category on the atheism/theism spectrum. An agnostic is a person who doubts if we can have knowledge of things we can't humanly comprehend, experience, study, see, or logically deduce (ie, the supernatural or a god). Saying "I'm agnostic, but not atheist" is like saying "I don't believe we can know something we can't humanly know, but I believe in something that exists outside of reality, that I can't possibly comprehend, logically deduce, and of which I know of no facts at all."