One point I made above deserves additional emphasis. Modeling. That’s the most effective, powerful means of teaching, and it is incumbent on every rebbe or teacher to use this. It goes way beyond the best mussar lectures.
To teach a talmid to apologize – the rebbe should apologize. This rebbe has zero obligation to wait for the talmid to do so first. This is not a bein odom lachaveiro issue, which might be the case if we were dealing with peers. It is rebbe-talmid. If this rebbe is worth keeping in a classroom, he should display the behavior of asking mechilah. This has nothing with who did it first or any other excuses. In order to teach someone to be a mentch, just show him how to be a mentch. If I hear any excuses about kavod haTorah to justify the rebbe not apologizing, I’ll throw up my breakfast.