Speaking of anti-examples for this thread, my favorite obvious result that is hard to prove is the Jordan Curve Theorem.Oh that is some dangerous stuff you got over there. That can end friendships! In fact it can even be a anti example to the thread, in that, it is very easy to contruct the problem and very hard to grasp why it works the way it does for a human brain that has evolved to survive in equatorial grasslands.
And, like the "Einstein tile" in page 1, this also is an example of false advertisement. The theorem has nothing to do with basketball.