A test is a class assignment. A paper is a class assingment. Turing notes into a class assignment--and especially mandating a specific format for notes--is counter-productive: it prevents students from taking notes in a format conducive to their learning. Notes are not a paper or a test: they're things for the student's reference.Requiring that a student takes notes is rarely harmful--I've known a few people who do can't focus on the lecture and take notes at the same time, but most people would surely benefit--but mandating that they take notes in your format hinders students in taking notes in a way most beneficial to the entire point to taking notes.Your analogies completely miss the entire purpose of taking notes, and so did the professor. Complaining that the professor should be fired was definitely an immature way of dealing with it, but that doesn't take away from the fact that the requirement was very misguided.
I've had a couple classes where the professors wanted to see students' notes, just to make sure we were taking them and paying attention. I provided the notes, but with a warning to them that my notes are going to be filled with the occasional shorthand, foreign word, or unexplained reference. If the professor needed me to rewrite my notes in a readable format, that meant an extra writing assignment for each day of class, as I couldn't take notes that are both legible to others and useful to myself fast enough by hand (and at the time I had no laptop). Demanding that I write notes in their format in class would be tantamount to demanding that I don't pay attention to half the lecture. How is that sane?