First, Christians do NOT argue that because an atheist cannot disprove that God exists it is, therefore, rational for us to believe in God. No, instead we provide what we believe to be very rational bases for a belief in God. We provide what we deem credible EVIDENCE for the existence of God. It is just that the atheist does not accept such evidence. The real question is why the theist accepts such evidence, but the atheist refuses to accept such evidence.
I can tell you why I believe in God... yet, I have a hard time ever pinning an atheist down as to why they do not believe in God. Rather, the consistent refrain I hear from atheists is, "you cannot prove it scientifically, therefore, it must not exist." Which brings us to the second and most important point. Namely, it is the atheist who is guilty of making an argument from ignorance, not the theist. If you think about it, when the atheist says, "You cannot prove God exists, therefore He must not exist," this really is a form of an argument from ignorance that the atheists say the Christians are guilty of.
Andrew, you say that I have not answered your questions. I believe, actually, that I have and that you have yet to answer any of my more basic arguments. For example, explain to me:
1. How is it more rational to believe that the earth came from nothing than to believe that God created it?
2. Similarly, given the immense complexity of our bodies, of nature, and of the universe, how is it rational to believe that these systems were not designed?
3. What is your basis for morality if you truly believe there is no God?
4. With some notable exceptions, a belief in God tends to make people better. Why will you not accept that as proof of God's existence?
5. It seems that your standard for truth is science, yet I believe that science (a) does not answer every question, and (b) actually points to the existence of God. Why do you believe differently?