Years ago I saw someone doing a community outreach lecture tour, for Next Generation Science Standards. On behalf of NSF I think. She was getting hostile questions, many of the too-broken-to-even-be-wrong variety. Ones where normally I'd just shake my head, perhaps think "nutter", and hope the speaker was able to move on without getting bogged down.

She addressed the questions with a grace, and insight, and empathy, that was awesome to watch. I'd not have thought it possible. I wish now I knew who she was, and had video. If anyone knows of this skill set being taught, I'd love a pointer.

So I no longer think of the quality of a question, and of a questioner, as being a worthy bound on the quality of an answer.