So, where does Atheism fail? That answer is really quite simple: from the beginning.
Atheism starts out by taking an illogical position and assumes it to be true.
The Atheist will say "gods don't exist", and when I ask for proof of this truth claim, I'll be told "You can't prove a negative" and "the burden of proof is on the believer". Not only are these brush-offs both fallacies, but they fail to address the reason for God's supposed non-existence.
Both Richard Dawkins, the great Evolutionist, and Christopher Hitchens, the Vanity Fair opinion writer, tried to prove Atheism in their own ways. Dawkins did a horrible job of making his case and proved his field is science, not philosophy. Hitchens wrote a bitter polemic against God's existence but didn't quite state that God isn't real. He at least was still willing to consider the matter up to the point of his death from cancer.
But the problem for Atheists remains: there is more evidence for the existence of God than there is proof that God isn't real. And even worse: lack of proof (as Atheists claim) doesn't make their case. If a murderer erases all the evidence, does it mean the crime never occurred? Atheists have a real conundrum here, and yet most of them refuse to admit that it takes faith to believe in Atheism.
Faith.
Remember that. Atheism may require even more faith than belief in God.
'Nuff said.