I agree with Xqby (in the thread linked by SDG is his post 4) about this. His definition might be simplified thus: to pigeonhole is to categorize something according to a narrow range of attributes. For me the person criticized usually is the person who pigeonholes; the suggestion is that they have a quite limited series of categories into which they fit the people they know. Thus they lose the individual characteristics which make people interesting and, sometimes, endearing.
So here I wouldn't say we pigeonhole people. It's a dangerous generalization and it's to present a very narrow view of human life. I would prefer some people like fitting people into categories, which is much less pejorative to my ear. In the specific case I'd simply say I reckoned he was a good teacher - the formula in the OP suggests that good teachers are all similar, like Tolstoy's happy families.