Hah, they didn't even notice how Maybe is algebraic and State is coalgebraic ...
(I completely made this up, it could be true according to my limited understanding, but more likely it's completely wrong.)
I think the confusion comes from a different source: Obviously, Monads are an extremely powerful interface. But such an interface only make sense when we have some form of hiding of implementation details: As long as I know the constructors of Maybe, I can completely ignore or reinvent the monadic functions. So State is actually the better example here, because in a paramatrically polymorphic type system, we don't know anything about the concrete state when implementing return and flatmap. We need a composition technique that works for every possible state.
So unless your language has a parametric type system and/or allows for hiding implementation details, you won't ever benefit fully from and thus never grasp an intuition for monads.
(I completely made this up, it could be true according to my limited understanding, but more likely it's completely wrong.)
I think the confusion comes from a different source: Obviously, Monads are an extremely powerful interface. But such an interface only make sense when we have some form of hiding of implementation details: As long as I know the constructors of Maybe, I can completely ignore or reinvent the monadic functions. So State is actually the better example here, because in a paramatrically polymorphic type system, we don't know anything about the concrete state when implementing return and flatmap. We need a composition technique that works for every possible state.
So unless your language has a parametric type system and/or allows for hiding implementation details, you won't ever benefit fully from and thus never grasp an intuition for monads.