At a glance, choice seems obvious because every nonempty set has an element, so taking one element from each set in a collection looks like a perfectly reasonab

At a glance, choice seems obvious because every nonempty set has an element, so taking one element from each set in a collection looks like a perfectly reasonable thing to do. For well-ordering, it asserts a property that people are typically not taught to treat the reals as having. "Everybody knows" that a set of reals doesn't necessarily have a smallest element. The "next-largest"/"next-smallest" construction is something you see a lot in (mistaken) attempts to prove 1 ≠ 0.999…. My usual experience is that people presented with well-ordering principle try to figure out how it works with the reals -- what is the order relation? It seems like asserting the existence of this structure pushes them into a more constructivist mode of thinking, whereas they don't typically feel like they need to come up with a way to construct choice functions. Zorn's lemma deals with a setting that has somewhat more structure to it, so it doesn't really seem obvious whether it's true or not.