> But what's the difference between an example ("it’s such good pedagogical practice to demonstrate examples of concepts you are trying to teach") and an analogy ("now they have to spend a week thinking that monads are burritos and getting utterly confused, and then a week trying to forget about the burrito analogy"), and why is it completely subjective leaving us with no hope?

I think it's not that there's a difference per se between an example and an analogy, but rather that one has to recognize that even the best-chosen analogy or example won't save other people from having to go through the struggle to come to grips with a difficult concept. That is, from my point of view, the problem with "it's so simple, a monad is a burrito!" isn't especially the "a monad is a burrito" part (although I'd argue that that's an overly fmap-flavored analogy, it's not really the point); it's the "it's so simple" part. From this point of view, which is mine as a teacher, teaching isn't a process of finding the path that lets students avoid every difficulty, but one of helping them to avoid the avoidable ones, manage the unavoidable ones, and build their own mental maps so that they can eventually understand and navigate the terrain themselves.