Faith is that, yes. But you're missing the point. I can have complete faith in my mother's infallibility, then list multiple proofs that my mother is infallible. I can do just that with God. In fact, atheists put their faith in science. It doesn't mean that they're not allowed to prove their own point.

Some logic isn't really valid reasoning. It's not really logic. I believe the fallacy committed here is called the false cause.