[lmm]

I think that's largely because mathematics abstracts more than is obvious. My favourite example is Hilbert's basis theorem, which looks like it's not even a question until you realise how general the notion of "space" that it applies to.

[gohrt]

Right, same reason that the Banach-Tarski paradox is intuitively baffling. It relies on fractal-structures that require uncountably-infinite fine detail.