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.