I don't think this story is about a teacher who isn't good at "just" the fundamental actions of teaching. It sounds like their actual skill and respect for the

I don't think this story is about a teacher who isn't good at "just" the fundamental actions of teaching. It sounds like their actual skill and respect for the material is lacking. If your math professor couldn't prove the basic theorems he wanted you to memorize without referring to his authority, that, to me, would be a sign not that he was bad at explaining but that he was fundamentally unskilled in his field.