A (small) minority of mathematicians find it unintuitive too. Intuitionistic mathematics and constructivist mathematics say that if you can't construct an example of it you can't prove it exists. They don't accept a proof that "some X exists such that P(X) is true" as valid unless you can give an example of such an X. "Intuitionist" because it is based on an intuition widely shared by a lot of people, but mostly rejected by modern mathematics.