Showing the proofs to the theorems taught in university-level math classes is expected. For starter, being that there can be many proofs to the same result you

Showing the proofs to the theorems taught in university-level math classes is expected. For starter, being that there can be many proofs to the same result you can't expect the teacher to show them all. Opinions also differ on what is valuable and should be taught (you can't teach everything in a finite time), if the teacher can skip some partial result he doesn't find interesting he can opt for a different proof altogether. Thus there'll always be some treasure left for the most ambitious student by tackling various such works.