Because especially for harder problems there were probably dozens of mathematicians who studied the problem for centuries in order to find those derivations that your teacher presents to you.
In my school math education we had the standard that everything we learn get's proved. If you are not in the habit of proving math, students are not well prepared for doing real math in university which is about mathematical proofs.
In general the math that's not understood but memorized gets soon forgotten and is not worth teaching in the first place.
That's a great rule, but it still has to have limits. Otherwise you couldn't teach calculus without teaching number theory and set theory and probably some algebraic structures and mathematical logic too.
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: