I think we ALL know that there is no way to prove that god doesn't exist...
In fact if the theist is a complete brain case, he could believe that the entire universe was created two days ago, and god just made everything seem like it has been here for millenia. And there would be no evidence against that claim. or the claim that fairies exist, or invisible pink unicorns...
But unless the theist is that stubborn, there are a bunch of things that would support the claim that god doesn't exist:
Like the flaws in design, if I was supposed to live forever, why do I only have two sets of teath? If I was never supposed to get ill, why do I have a cough reflex, or have and immune system? If all the carniverous animals are supposed to eat grass, how will the earth not be over infested with bunnies? If the earth is supposed to be inhabited forever, why is the moon, slowly getting farther and farther from the earth? If there was no big bang, why are the gallaxies all moving away from a central point in the universe?
Obviously all of these things dispute the belief in the god spoken of in the Bible. Lot's of people make up their own definitions of god, but I won't even attempt to dispute these because as I said, they are made up and therefore if I came up with something that indicates they don't exist the person will just change his definition of god to prove me wrong... sorry your on your own with that.
But ask yourself: Do you believe in god because it's logical to do so, or do you believe in god because you want to?
If you want to believe in god that's your problem, but personally I think the whole concept is flawed.
LtCmd.Lore