This is exactly what I was talking about. This is a classic atheist response! And it is false. Essentially, the atheist who asserts that he doesn't have to prove a negative, that he doesn't have to prove God doesn't exist, is saying that he doesn't have to offer any justification for his position. But if the atheist has no justification for his position, or is unwilling to offer any, then why should anyone give it any heed?
If we have three people - a Christian, an atheist, and a seeking agnostic - and the Christian offers proof of God's existence to the agnostic but the atheist responds to the agnostic with "I don't have to offer justification of my view that God doesn't exist. One cannot prove a negative," who do you think has properly justified their viewpoint? Certainly not the atheist!
As well, negative, universally-quantified statements
can often be proven (and are). For example, a negative statement such as, "There are no deaf piano tuners," can be made quite reasonably and, for obvious reasons, is clearly true. In many instances where I make "all" or "none" statements about a particular domain, I can prove a negative. "No circle has right angles," is another example. I can look at all the circles I have within the domain of my knowledge and see that none of them has a right angle. It is therefore reasonable to assert that all circles have the same geometry. And so on. Clearly, then, it is
not true that one cannot prove a negative statement.
Finally, the atheist's declaration that atheism is simply the absence of any belief about God amounts to a kind of psychological report on the state of the atheist's mind that trivializes the atheist's position. Dr William Lane Craig writes,
"Such a re-definition of the word atheist trivializes the claim of the presumption of atheism, for on this definition, atheism ceases to be a view. It is merely a psychological state which is shared by people who hold various views or no view at all. On this re-definition, even babies, who hold no opinion at all on the matter, count as atheists! In fact, our cat Muff counts as an atheist on this definition, since she has (to my knowledge) no belief in God."
If this is what you really believe, then I have to tell you that you don't understand your own viewpoint. In fact, atheism necessarily entails these four points. They arise unavoidably from (especially naturalistic) atheism. That you don't realize this suggests you have a very superficial grasp of what it means to be an atheist.
Selah.