Many (I'd say most but I have no statistics to prove this at hand) young men and women in high school have absolutely zero clue what they'll end up doing for a living. You can't possibly know what you didn't need to know until much later in life, and at the very least learning something as functional as complicated math makes your everyday math that much easier to do.

If you're counting on 14, 15, 16, 17, and 18 year olds to confidently choose what they should learn and stick with a program that'll lead to their career, all you cause is great depression as they hit their 20's and realize they want to do something completely different. So yes, the "liberal arts" approach may lead to some "useless" information; however, it teaches you all the possibilities of things you could pursue interest and mastery in. It also prepares you for the most amount of possibilities. Because for something like Engineering, you'd be pretty screwed to decide "Oh yeah I want to do that" if you elected not to take pre-calculus in high school and you're just now catching up in college.