It's easy to gain physical intuition because you can often explain one physical phenomenon in terms of another physical phenomenon that you have much more real life experience with.
But with mathematics, "intuitive" analogies are all in terms of other mathematical objects! You can't build intuition if you don't even know what they trying to abstract over.
In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated.
The story defined scissor statements as ones that simply make two ideologically incompatible groups realize the "other" is hiding amongst "them".
Close contact and narcissism of small differences means fighting will naturally ensue.
For example the statement that "You should wipe your butt standing up" (or sitting down). Neither side knew the other group exists, and once they do they will automatically start ridiculing each other: you're doing it wrong, weren't you raised properly, etc.
A more serious recent example is "feelings matter in open source". Coworkers you previously respected can instantly become enemies because you didn't realize they were monsters.
Unlike the short story, I think these scissors are somewhat healthy. I have faith that people are drawn to controversy because deep down they want to resolve the dissonance. So eventually one side will win and the fighting will stop.
But with mathematics, "intuitive" analogies are all in terms of other mathematical objects! You can't build intuition if you don't even know what they trying to abstract over.
In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated.