Instead of actually making that point, he quibbled about the specific labels you mentioned.

I really hate to defend this smug atheist, but those labels were important in the context of the debate. If JP refuses to identify as a Catholic, or even a Christian, then he has no anchored principle to even make a point against in a Christian vs Atheist debate. How can you even begin the conversation if every presupposed position is suddenly "nu uh, I ain't that either!"

So without the labels, JP is just waffling badly. With them, he fails as a Christian by denying Christ and doing so for some beneficial purpose. I guess to not be attached to the baggage of the label.