Two contradicting propositions cannot both be true when one proposition is the direct negation of the other.
This invokes two of the formal laws of logic, Excluded middle and the law of Noncontradiction.
Atheism and Theism is a true dichotomy. Atheism is a lack of belief in a god/Gods, Theism is a belief in a God/Gods.
Now where does that leave agnostics? Agnostics claim that knowledge of a God is unknowable. But is it possible to believe in something that is unknowable? Assuming that the matter is truly unknowable I have to answer yes (it is otherwise known as faith). Therefore the word agnosticism is not mutually exclusive to the terms of atheism and theism. One may call themselves an agnostic and be a theist or an atheist.
But, what about a person who professes no belief in a God and calls himself an agnostic? By default that person is shoved into the true dichotomy of Atheism and Theism, and must label themselves as an atheist, whether he/she likes it or not.