This kind of argument can always go further by removing abstraction… you could argue that you don’t understand the chain rule without understanding the quotient

This kind of argument can always go further by removing abstraction… you could argue that you don’t understand the chain rule without understanding the quotient and product rules which are used to prove the chain rule, and then once further with the epsilon-delta proofs required to get limits going for the derivative in the first place, and then continue until we reach some axioms. I think you can accept that the chain rule is a thing, without understanding it, and then go further to understand its application to backprop.