I haven't learned any general relativity yet, but from what I know of special relativity, it actually makes perfect sense. You start with the assumption that no observation can allow you to deduce where you are or how fast you are moving, and then follow that premise to its logical extremes.

There are things, if you look at them hard enough, you can understand it intuitively, and they cease to be weird.

Quantum mechanics, on the other hand, is one of those things that even if you look at it really, really hard, you still can't understand it. So no, I think quantum mechanics is the only example you could have used here.