It seems like this is exclusively how (most) people teach graduate/upper div math classes. They go through the proof of some big theorem, sometimes it might take two lectures. It's obviously important. But I honestly have no idea what I am supposed to be getting from this. It honestly seems useless to me. I know it isn't. I know it's a rite of passage to prove xyz theorem. But is this really worth sometimes two class periods?
I honestly don't know what I'm supposed to be learning. These proofs require unique logic a lot of the time, and this logic is difficult to transfer to other problems.
In lower div classes, it would be informal explanations of things followed by a lot of examples. I'm not saying that that's the way to teach functional analysis for example. But at least it made sense to me. I know what I was supposed to be learning.
I can go through all the details myself, I go to lecture for motivation/intuition/things you can't normally get from a textbook. The proof of Riesz representation theorem for example can be found in any text. Why can't I just read it on my own? It's much easier to read proofs like this on your own rather than in class.