Which apparently men, with the best will in the world, just cannot perceive.

At least it seems that goodwill isn't sufficient to make it possible for them to perceive it. I won't make blanket statements about what men can or cannot perceive for the same reasons that I don't like to hear men make blanket statements about what women can or cannot perceive; there are always exceptions to any broad categorical statement (including, doubtless, the one I just made about broad categorical statements, if you want to play paradox games). But there's a difference between blanket statements and statistical predictions, and when I'm deciding what to do, between choices that are mine to make, such as scanners with random viewers I don't see or pat-downs by female agents I do see, I will bet the short odds.