The true definition of Atheism
What I am actually going to do in this first bit of the discussion is not tell what I think is the true definition of Atheism. What I am going to do however is point out that I have noticed in some discussions involving Theism and Atheism some people somewhere along the line get stuck and start arguing about definitions.
Now, instead of trying to refute each other's idea of how something is or should be defined I think a much more pragmatic approach should be for both parties to come to an agreement on an idea about that "something" so it can continue to be explored.
So for example, if you are an Atheist defining Atheism as a lack of belief instead of the outright denying of the existence of God and a Theist claims your definition is flawed then invite the theist to accept or at least entertain this definition and then explore it.
The burden of proofs
So in an argument about the existence of God does the burden of proof rest on the Theist or the Atheist? Now, if the Atheist in question is someone that claims there is no such thing as God then the burden of proof rests on both the Atheist and Theist as they are both making unfalsifiable, untestable claims.
If on the other hand, if the Atheist is someone that doesn't deny the existence of God but doesn't believe in God either because they see no good reason as of yet to do so, then the burden of proof will always be on the Theist who outright claims that God does exist. Without Belief does not equate to the denying of something or believing that something doesn't exist; without belief is simply that; without belief.
Also, after reflecting on this for a bit I've thought that if I myself was a theist I'd more comfortable debating someone that denies the existence of God as it gives me the opportunity to put the burden of proof on them first. You can't do this with someone that is simply without belief; it's like asking a silent person to prove something they never claimed. Hence, I also think this why some Theists that I've witnessed from my experience start resorting to having arguments about the definitions; it makes their position much easier to defend.
The unexamined thought is not worth thinking.