Teaching someone how to do the skill is a different skill to being able to do the skill, and it requires a more thorough conscious knowledge of how to use the skill than using the skill does

Even more than that: it requires the ability to communicate that conscious knowledge to the other person (thus, a two-place function). Each of us has our own internal "programming language" that determines which words or thoughts correspond to (e.g.) which bodily movements, and furthermore we tend to have our own specific repertory of bodily movements that we're used to making without thinking, which may not be the same as another person's. A teacher has to be able to bridge this gap -- which, in particular, requires awareness of its existence in the first place.

(Analogues of this hold for less physical tasks, e.g. doing calculus problems.)