This rings so true for me. Lot of teachers has this ass backwards style of teaching where they will come up with final formula like deus-ex machina. Why? To buy his text book where it is explained the way he wants it.
But that often expects that the person explaining a thing knows what they are talking about. I.e. people on high school does not like logarithms because they don't understand what it is for. I would bet that's because teachers themselves have absolutely 0 clue what in essence is a logarithm and why did it came to be. It was centuries of research, which you can summarize with one sentence - to make multiplication as simple as addition with lookup tables, because at 15th century they did not have calculators so multiplication was a hard laborious process. 135+265 is simple. 135*265 is difficult.
Given a flood of results, you look at the most promising results and then figure out how they work, not the other way around.
Almost all successes are built on having knowledge of a desirable outcome first and foremost, rather than the means to obtain them.