I am finishing my undergraduate degree and one thing I've noticed is how little weight has been placed upon the ability to read proofs, in basically all of my math courses. In first year calculus you are shown the proofs for things like the limit of sin(x)/x at 0, but in my experience there is no incentive for you to understand them. This pattern continued even in more advanced undergraduate courses on foundations and real analysis. As one example, the professor spent an entire lecture proving the schroeder-bernstein theorem, and very few students made an effort to understand it (they certainly weren't motivated to do so through grades). Generally speaking, my classes have followed a format where the professor will prove theorems for a significant portion of the lecture time but tests are designed with applications and proof-writing in mind and certainly most proofs done by the professor are far too hard for a student to recreate independently, so there is no incentive to learn the details of the more complicated proofs.
This seems unusual to me, considering the format of most courses requires you to understand the arguments backing up a particular proposition. Is this true of most university programs? Should a greater emphasis be placed upon learning how to read complicated proofs?
When I was doing my undergrad your experience is the same as mine, so I guess things are kind of similar in undergrad programs. The motivated student can understand and do the proofs of his/her own but the exams are designed to only know whether the student understood the material covered in the class and whether (s)he could apply them for a given problem.
That being said, in my transition to grad studies I have noticed a significant difference. Here more emphasis is given on proving theorems. Sometimes they even give a theorem that is not covered in the class to prove in the exam. Most of the time the proofs that we have to carry out in exams aren't so difficult compared to what is done in lectures, but yet I feel it quite tiresome and difficult with regard to the very little experience I have had in proving theorems in my undergrad days.