It is easy to set up a straw man argument against atheism, as the OP does, in which atheists are portrayed as saying that "they can prove the non-existence of God."
Atheism, as I understand it, and from the atheists I know, is the position in which one _does not_ believe in the existence of god/s. One chooses not to believe.
The non-existence of things cannot be proven; the burden of proof lies upon those that believe--they must prove that something exists. One cannot prove the non-existence of the tooth fairy, nor the great spaghetti monster in the sky.
I am atheist, and agnostic up to the point that even if god/s did exist, it bears no relevance to my life. It does not and would not affect me. If the tooth fairy were suddenly to be proven to be real, I would continue on with my life the same way.