Most people aren’t practicing teachers, so it makes sense that not all explanations are the best. Trying to get an intuitional understanding of passing by reference or passing by value in imperative languages is arguably more important than understanding how map works, and yet I’d argue it’s also harder to do.

If you understand map (not just lists, but futures, IOs, Options, Maybes, etc.) then you understand Functors. Yes there are laws, but mathematical laws here are just encoding our intuition. Something like Iterator in Java may not have laws, but you would expect that calling .next() doesn’t modify an SQL database, though it wouldn’t be a technically invalid implementation if it did. The same is not true for Functors. If you map over a List and the act of mapping each int to its double modified a database then you wouldn’t have a lawful functor. But that should make sense intuitionally without knowing the laws.

People in OO land are more happy to say they “understand” something if they generally get what the abstraction is going for. Do you know all the methods for Iterator/Iterable in Java? Even if you didn’t, you’d likely say you get the “point” of an Iterable. The bar for understanding things in the FP community is usually higher than just understanding the point of something.

This doesn’t mean FP is more complicated. Actually it kind of means it’s simpler, because it’s not unreasonable for people to totally understand what Functors are for all languages that implement them. The same is not true of Iterable/Iterator. There’s no way you’d have more than just an intuition about what Iterable is in a language you don’t know. I don’t program in Agda or Idris, but I know Functor in those languages are the same as Functor in Scala and Haskell. Same with Monad, Monoids, etc.