I had a math teacher in high school who, when I asked why I had to learn the quadratic equation, answered with an asinine anecdote about someone asking her to recite it in a social setting. Mathematics felt similarly arbitrary to me at that point, and I was turned off to it for an unfortunately long period of time.
One of the ones who was also held in fairly high regard in the school once got into 'time being relative', and trotted out, in the same sentence, something about experiments showing time being different at the poles and the equator, as well as something about time in "latin" cultures. That drove me up the wall!
The most common question out of a student's mouth is "But why do we have to learn this?" And that's a pretty good question.
Unfortunately they're asking the people least likely to know. Teachers don't even know why most of these things are important. They learned them at school, and then they grew up and taught them, but they never passed through the stage of actually putting them to use in any other context.