Ok, let's take it step by step. You may agree with part of what I will say, but this can be addressed to anyone... And do know before hand that I agree that science, logic or reason should not "lead" to atheism. But here is why:
We come to life with no belief. When we grow up, we are told about a god. We believe that or we don't, it is not a choice. If it was a choice, we'd simply believe or stop believing at will whenever we need it. Now, when you don't believe, you are called "atheist". But it doesn't really matter for the one who doesn't believe to be called anything really. We may as well give a name to people who don't believe in every specific thing (ghosts, aliens, Santa, whatever). So the word "atheist" was given to unbelievers by believers. I don't believe in any god, but I don't have to call myself anything because of that... If someone wants to call me atheist, fine, I don't care, it's their choice. That's just to say, I don't need to justify anything. I didn't believe your story, that's all. If you wanna know why, find out how the brain works, that's all I can say. Now, I don't agree that atheism is based on belief just like theism. Like I said, we were just given a name because we didn't belong in their group, that's all. Do we have a belief system to justify everything we don't believe? I don't think that your non belief in Santa is based on any kind of belief system, is it? It just doesn't make sense to you, final.
For the "anyone without a belief in a god is an atheist" stuff, it's pretty irrelevant to the subject I think. Still, from what I know, an atheist doesn't necessarily say "there is no God". For example, I don't believe in God, I honestly don't think there is one, but I will never pretend to know there is no god. I even go further saying that it is possible that there is a god, simply because I have no proof for either side. But, I do consider myself an atheist as I do not accept the existence of a god. Would you say I am not an atheist? Before you answer, please, don't tell me I'm an agnostic. Agnosticism has to do with knowledge, not gods. Saying you're agnostic simply means "I don't have the knowledge of..." So you can actually believe in a god but still say you do not "know" that he exists. In my case, I am an atheist because I don't believe in a god, and I'm agnostic as well because I don't know the answer.
So all this is why science, logic and reason don't matter. You'd still be an atheist or a believer without them. But what I think happens is that, when they are already atheists, then science, logic and reason only go against beliefs. Like, when you hear someone say the Earth is 6000 years old, you tend to reject that person's beliefs because he/she goes against a basic scientific fact. Science, even though it is not 100% reliable, still makes way more sense than beliefs. So when I use science or reason or logic to think, it just systematically goes against beliefs and this may "look" like a reason to be an atheist, but it's really not. You are or you are not an atheist, the rest only goes for or against beliefs.
I hope I'm being clear and not off subject.