I find that for me, and many other people I know in the mathematics department of my university, once infinities, uncountability, and such enter the picture, the accuracy of intuition quickly starts to diminish, so it's wise to be careful and make sure the proof is complete before declaring it obvious. As a good example, note how surprising and notable Cantor's diagonal argument seemed the first time you heard it- it isn't obvious that the reals aren't countable when you don't already know that, so you might start trying to construct a counting scheme and end up with one that "obviously" works.