The professor seems to understand the difference between the full complexity of the real world and a limited educational exercise with a manageable scope. Mr. Melon does not understand this and seems to only be able to engage with the real world at full complexity. The professor is completely open about the fact that he’s running an artificial scenario with a limited focus. Mr. Melon just lobs confounds at it repeatedly. I will have to say that the professor is in the right here.

But because the professor has a british accent, glasses, and a bow tie, he’s coded as an elitist prick. And Mr. Lemon’s vernacular, colorful clothing, and casual style is supposed to contrast with this in a classic “book smart” versus “street smart” trope. In fact the entire movie is built on this premise: real world wealth and popular appeal help Mr. Lemon triumph over age, social hierarchy, institutional rules and many other obstacles to achieve social success and the attention of eligible young women. Therefore, in the language of the film, Mr. Lemon is most obviously “right.”

I wrote this mainly to reassure myself that I was not in fact having a stroke while reading the OP’s title.