Plenty of things are intuitive if you have the right mental model backing it. I'd wager some folks thing of all/any as "at least one True"/"Everything is true", which makes it a trickier think.
Mental models often get spicy with empty/"corner" cases. This isn't quite the same, but a lot of kids struggle with division as sharing rather than division as measuring, which makes division by a number less than 1 conceptually difficult. http://langfordmath.com/ECEMath/Multiplication/DivModels.htm...
all: no false elements any: not all false elements