"The problem here isn't a lack of logic. The problem here is what, for want of a better term, you might call a shortfall of logic itself. Our logic is unable to prove a generalisable absence; the total lack of something. You and a friend could be discussing the most outlandish thing either of you can imagine - something you can be pretty sure doesn't exist, as the pair of you made it up only moments before - and our logic will be unable to prove that it doesn't, hasn't, couldn't or will not exist somewhere at sometime.
I say 'our logic' because the shortfall is not in logic, but rather in us. Logic is a process rather than an end result; you put garbage in, you get garbage out, and it's not the fault of logic. If we had complete knowledge of everything, logic as a process could be used to prove the absence of something. We don't, so we can't use it to disprove the existence of God. Our knowledge is less than full and complete, so the information we feed in has to be less than complete. Logically, then, the conclusion we get will be less than conclusive.
Does atheism thus require 'a leap of faith'? Well...yes. But I would hesitate to liken the size of the leap to the one required in theism.
We believe in lots of things we've never seen. I've never been to Kuala Lumpur, but I believe it exists. We also don't believe in lots of things we've seen; all of us here know what a unicorn looks like, but none of us believe in them.
I agree that atheism is not a position which can be fully logically supported. But it can be rationally supported, using a balance of probabilities based on known science, sociology and history. The 'leap of faith' I make to believe that Kuala Lumpur exists without personal experience of it is tiny; the leap I make to believe that unicorns don't exist is miniscule, and of the order of the one I make not to believe in God.
Logically, therefore, we imperfect beings cannot disprove the existence of God. Sensibly, however, probability and rationale dictate that we are more likely to be correct in atheism than theism - at least by the terms defined in Christian theology. A true position would be agnosticism, but not 50/50, sitting on the fence, vacillating agnosticism. Informed agnosticism says we can't know for sure...but it's doubtful..."