Your approach will not work. Either continue attempting proofs or give up. It's fine to read the answers after you've tried.

> I've heard many many times that you can only learn math by doing it, which is certainly true

yes

> and is akin to saying that you can only learn a language by...

no. this is you evading the main point.

Taking a graded class with homework can help. So can finding an elementary book on a subject that interests you (topology, combinatorics, algebra, ...). Linear is dry, that may be your issue.