A implies B does not mean B implies A.

I see failure to understand this in all sorts of critical thinkers.

this is fundamentally not true. while math has a tone of rote learning in the same sense one may learn grammars in their native tongue over time, formulating proofs or fluent articulations of quantities involves the same problem solving and critical thinking one also applies to thoughtful communication.

math is communication, and the deeper you go, the more fluent you become, and the more open ended your application gets because you are problem solving, which is a direct consequence of applying critical thinking skills -- you have to consider your solution against a set of possible solutions, and determine pros, cons, and also attempt to disprove your own ideas.

wild statement.