I have never once in class found out how or why the formula's and expressions and equations were created.
The class you're looking for is a "Sets and Logic" course. It's usually taught as a prerequisite to an introductory discrete math course in university.
Years of high school education convinced me that math was nothing more than a rote excersize in symbol memorization and manipulation, but taking that class completely changed my perspective. It covers the logic used by mathematicians in explicit detail and builds mathematical intuition that helps students see how equations, theorems, etc... are created from the mathematician's perspective.