I'm the same way. At university, I had an instructor for Calculus I who seemed content with just having us memorize formulas and identities and "shortcuts", only to regurgitate them on demand. I barely passed with a C-. Then, I had an instructor for Calculus II who was much the same. I made a D+ in Calc II, which, since Calculus I-III are considered essential courses for engineering students, was not passing. My second time through Calc II, I barely passed with a C-.

Then, I get to Calculus III, and my instructor introduces each concept by showing us a complicated-but-ultimately-intuitive formula for something, then deriving the "shortcut" step-by-step. While most of the students griped that it was boring, I found it quite interesting, and for the first time in my university career I felt like I could grasp calculus. I made an A-.

There are other instances of this, as well, but that one was probably the most dramatic. I don't know what it is. I came up with a handful of analogies just now, but none of them seemed particularly satisfying, so I gave up. Perhaps it's just a quirk, I dunno :)