Huh, I'd never thought of the DM (or referee / umpire, this is directly inherited from wargames) being conceived in the early days as a teacher making up problems for Prussian officers in training students to solve, hence the Gygaxian adversarial DM style.
And the benign version was "the problem is hard or deliberately misleading, but for the purpose of making the student better", while the less benign version was "the problem is hard or impossible to solve, and the student doesn't learn anything, so the teacher is bad".
I find this fascinating. To be clear, I don't want it anywhere near me, it's the opposite of my jam (it's a bloody roleplaying game, not homework), but I do understand it, and it's very interesting, and it explains SO MUCH about oldschool DM, err... arrogance.