A = Without. Theism = God.
Atheism = Without God.
So not having a God that you believe in, doesn't give you a stance in believing there is no god, or not believing in the existence of god. If you take the word existence out of the equation then you have a better definition. It's a simple word with a simple meaning. I don't hold a belief in a god, so I am atheist. You could throw yourself under the definition if you firmly believe there is NO god and that is your stance, but that does not define atheism. See what I mean?