Conversation

Mathematicians describe points on the plane with coordinates (x,y). The first coordinate says how far 𝑎𝑐𝑟𝑜𝑠𝑠 you go and the second says how far 𝑢𝑝 you go. Then they describe entries of a matrix Mᵢⱼ with indices where the first says how far 𝑑𝑜𝑤𝑛 you go and the second says how far 𝑎𝑐𝑟𝑜𝑠𝑠 you go.

In each case I've had teachers who insinuate that this is the only reasonable thing to do and you'd have to be nuts to dream of doing anything else.

I think some teachers don't distinguish between facts and conventions. Actual facts of mathematics are worth thinking about - understanding them more and more deeply is a never-ending quest. But for arbitrary conventions, you should just memorize them and move on.