I don't mean to say that we need to be extremely strict with how classes are defined. Using your example, you say you would be annoyed if wizards were set to all come from a wizard's college. Learning spells through long hours of study and application of logic and rigor naturally fits a background of going to a wizarding school, but it doesn't lock you into it. You could just as easily have a wizard that found some ancient tome, and spent hours learning spells from it instead of learning from a teacher. Or you could have one who discovered magic independently, or maybe you learned your craft directly from a master, or any other of many different possibilities.
However, as different as these background sound, they all agree that the Wizard picked up certain skills while he was studying. They agree that he has a spellbook, that he learns magic from study, that he can cast rituals, and so on. I would say that the Thieves' Cant falls into this category as well.