I believe this can apply in the reverse also, no? A non-believer asking for proof when his/her mind is already made up about the non-existence of God.
The difference is that we weren't born non-believers. Almost everyone carries a belief system very similar to their parents. Muslems tend to stay Muslems. Mormons tend to stay Mormons. Hindus tend to stay Hindus, etc. It is the rare person that can examine their belief system and find it flawed. You are a Christian, and you were raised a Christian, albeit a different denomination. That doesn't mean that it is impossible that your belief system is correct, but it does mean that someones opinion that has examined their belief and disagreed with it carries more weight. That person's belief system is not based on the blind luck of the philosophy they were raised with.
If you were born an Aztec you would believe fervently in the snake god Quetzalcoatl. If you were born a Viking you would believe in Thor. If you were born in Afghanistan you would pray to Allah five times a day. You could use your rational for believing in the Christian god to believe in these as well. The same could not be said for me, nor for many others on this board. We have rejected the superstitions we were born into. My mind is not made up about the non-existence of god. If evidence could be produced for his existence, I could be persuaded to believe. I simply refuse to believe in anything for which there is no evidence. That is why I reject Quetzacoatl, Thor, Allah, and Jehovah alike. There is no difference in evidence for believing one over the others. There is only the accident of birth.