Yes, true insight requires a level of understanding usually obtained through a focused effort to understand all the components that make up the idea, several levels deep.
Explaining the end result -- the epiphany -- to someone else is often difficult because most will have gaps in their understanding that prevents them from seeing it they way you do and therefore they will have limited ability to verify and understand the significance of what you what you are saying.
Well that sounds like the problem of "I learnt it wrong the first time".
Looking back at issues I've had, learning it right the first time has been very important. If I've skimmed over some concept, and learned enough to apply it simply, when it comes to applying it more generally, I'm struggling. Going back and relearning it correctly takes time, and generally has to be done more than once.
Teachers should be careful to explain things simply, but ensure that the understanding really is correct. This can't really be assessed by exercise sheets, but discussion.
(Well it can by exercise sheets, by asking students to apply the concept to a different problem, but personal experience is only a few people make the jump without help. And when they get the help, that short circuits the learning that should have happened to allow them to do it themselves.)
