You can't apply maths as a test for it, you need someone who can tell you when you are wrong. It is not easy like a program crashing or an api returning an error, all errors when doing maths are entirely silent.

Lets take an example from the subject at hand, series in calculus: we want to prove that the sum of a series converges, how to you verify the proof without an instructor? Check that it is the same as the book? Most likely it wont be the same, proofs can come in many different ways. So either students start discarding their correct solutions thinking they are wrong or they fail to discard wrong solutions. Either case they fail to fully grasp the material.

You need to be a genius to properly root out all the errors in your head on your own, doesn't matter how many videos or books or tutorials you go through they can't evaluate your creative solutions like a real person can. Of course the need for instructors mostly disappear as you reach mathematical maturity, but to get there without help is extremely hard.