Explaining the fact that we exist

[chimp3]

This is a question that I wrestled with superficially when I first became an atheist. I was content with my answer to this question for a while, but after a recent discussion with a Christian friend of mine, the entire topic just became confusing to me. And, like I said in my introduction (http://atheistforums.org/thread-45867.html), I need some help when walking through difficult questions.

The question is this: "There were many transitional points in our universe's history that led to us existing. If one of them failed to produce the results that it did, we wouldn't be here, existing. Isn't it too much of a coincidence? Each transition point was against huge odds, and each of them was an extraordinary coincidence. How is it possible that we are existing against such overwhelming odds?"

I had a basic response to this like, "just because it's extremely unlikely, doesn't mean it can't happen", but I am not satisfied with the answer. Can anybody lead me through the basic thought process behind why we can exist against such overwhelming odds? I have my own thoughts, but I am willing, and needing to restart my thought process. 

Thanks!

Think of all the humans and other life forms that did not get to exist because that evolutionary line was snipped off by war, famine, predation, disease. Count us among the lucky few.