I love it when ignorant people say they're not ignorant when they're called such

Because that's exactly what an ignorant person would say. If they weren't, they would instead ask why they're being accused of such. That way they're showing they're at least open to getting the other person's perspective - open to the possibility that maybe they are ignorant about something and are willing to be enlightened. But just flat-out denying it and rejecting any possibility that they might be lacking knowledge in something, again, that's what an ignoramus would do. What's really funny about saying they're not ignorant is that if they truly are, then how would they know? Yeah, they wouldn't.