Axiom of choice

I find the quotes in Wikipedia's article on axiom of choice very amusing.

The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma? — Jerry Bona

This is a joke that although the axiom of choice, the well-ordering principle, and Zorn's lemma are mathematically equivalent, most mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.

Notice the use of the words intuitive, counterintuitive and too complex for any intuition. Even more fascinating, I also read that there is something called intuitionistic logic. Certainly, all these terms are not intuitive.