Given that we haven't constructed a decent AI, and don't know how those intuitions actually work, we only really believe they're not magic on the grounds that we don't believe in magic generally, and don't see any reason why intuitions should be an exception to the rule that all things can be explained.

Perhaps an easier lesson is that intuitions can sometimes be wrong, and it's useful to know when that happens so we can correct for it. For example, most people are intuitively much more afraid of dying in dramatic and unusual ways (like air crashes or psychotic killers) than in more mundane ways like driving the car or eating unhealthy foods, Once it's established that intuitions are sometimes wrong, the fact that we don't exactly know how they work isn't so dangerous to one's thinking.