Just curious, did you take other higher level math classes (complex analysis, topology, etc)? If yes, do you think they are easier?
It's unfortunate that many students studying math more causally or as a prerequisite for other fields don't get a chance to study Real Analysis because, in addition to this difficulty (from lack of exposure), it's also a great introduction to the beauty of mathematics.
I'm about as far as one can get from a practicing mathematician, but I still find myself pulling out the baby Rudin from time to time just for the pure pleasure of wandering through it.
25 years later I've forgotten most of it. But recently I've turned my attention to type theory, category theory, and related topics. I have little spare time and the amount of interesting topics to explore is daunting, but it's fascinating. (I've always been interested in mathematical foundations, too.)