Paul rebuked Cephas (Peter), the first Pope. By your logic, I guess he was displaying a "lack of faith."
For, until some people came from James, he used to eat with the Gentiles; but when they came, he began to draw back and separated himself, because he was afraid of the circumcised.
Peter was rebuked by Paul for his actions, not his teaching. If Pope Benedict goes on a murder spree, I'll rebuke him. It has nothing to do with teaching the faith.