@hug_of_war It’s difficult because thinking logically is a cognitive shift from everyday decision making that takes training for most people to be able to do. Such a course (ideally) shouldn’t be about teaching you about basic principles of logic, but about trying to train the student such that they can make the shift successfully and easily. Once you have the latter down, picking up some axioms takes but a moment.
It’s like working out a muscle you’ve never used. It’s extraordinarily difficult and painful, but seems like it should be so easy. It’s very tempting to just give up and say it’s impossible (most people do). Really, though, just like exercise you have to stick with it, because eventually you’ll get it with diligent work and attention (I know, because I taught proving things in Linear Algebra back in the day, and I suffered in this way back when I was learning how to do this). There’s really a concept called productive failure and it is all over learning to think with logic.
EDIT: @gorilla_paws Haha, and back when the Greeks had only logic to work with, they came up with some wacky stuff. I love it. Good answer, btw.