I cannot imagine a mathematics lecturer telling his students "a monad is like a burrito". Sometimes I think the analogies can actually hurt our understanding of something very abstract or novel, as is the case with the bad burrito analogy.
Well of course that's fatuous-- a math teacher's job in this case is to explain category theory. It would be professional malpractice for them to use an analogy to justify not teaching category in the interest of teaching practical programming techniques.
Actually, I always thought people were referring to Doug Crockford's talk about monads where he makes an offhand analogy to burritos at the beginning. In that talk the analogy has absolutely nothing to do with the 45 minutes of slides he presents, so it always struck me as weird. I had no idea bloggers had actually used a burrito analogy to explain monads-- I now realize he was making an allusion to that.
At any rate, in his talk he explicitly avoids both category theory and type theory in an attempt to explain monads to Javascript programmers for practical programming purposes.