Gee, if it can't be taught, you'd have to ask if it can be learned. And if it can be learned, then surely it's possible to create conditions conducive to that learning -- the practice and application you mention, for example.

I'm a big believer in the value of varied examples as a way to help build someone's competence / mastery / expertise. Whether formal university education is the right place to provide those probably depends on the university, the place within it, and the learner.

I do think you're onto something with regard to inferences, Harold -- some type of background processing that enables you to relate two things in a new way. Maybe that's the creation of a new pattern in your mind. Communicating that insight depends on similar data and connections being available to the other person. If I say that Agincourt was like the Alamo, except that at Agincourt, the Texans won, this inference falls apart if you don't know that both were lopsided battles.