I remember when we were taking an algorithm course, the professor gave us a proof question on the CLR book. It's a property of universal hashing and it used to be a well known corollary. It took me multiple hours to crack the insight that led to the proof. That level of teaching - the ability to select the right problems to nail deep concepts and to push us to grow - is hard to come by if we teach ourselves. At least not for ordinary students like me.