The next time someone asks you to prove that God does not exist, take him up on it. The "proof" lies in Goedel's Incompleteness Theorem. I mean, technically, with the challenge of "proving", the person has just:
(1.) accepted logic as a platform for establishing truth,
(2.) meta-mathematical logic has proven that there are propositions the truth of which are unknowable (Incompleteness Theorem), and thus
(A.) God is limited (there are things a god can't know the truth or falsehood of)
(B.) and by definition, God cannot be a god (because the definition of God is to be unlimited).
The proposition that a god exists has just been proven to be inconsistent, and therefore there is no God.
And we all know what happens next, right? The person rejects the logic, or decides he wasn't talking about logical proof, or rejects that God is bound by logic. In other words, the person will reject any bit of reason that conflicts with his pre-set beliefs, including reasons he had just asked for.
His request to disprove the existence of God was not sincere.