When I learned Algebra, it was 90% regurgitation of formulas and proofs you were expected to memorize. If you had a bad memory, you were screwed. I’m not sure how it is taught now, but in my time, both Algebra I and II were closed book tests and quizes so you had no access to any formulas or proofs. The teacher had the same difficulty. She would copy proofs from her notes onto the board, but could never solve anything without looking it up in her notes or in the book.
By my recollection, it was 90% factoring.
Algebra isn’t so much about “proofs” as rules; formulae. It’s like learning anything else....and what I always taught my kids: Learn the terminology (KNOW what the words/terms really mean), then learn the rules. Everything else falls into place. It really is that easy.