Kids in Jr. High & High School are still very impressionable. I think they should make a lot of peripheral courses optional, but I think the Core should be English, Science, Math, Phys Ed, & Home Ec. Home Ec should also focus more on stuff like managing a home, bills, mortgages, responsibilities, etc.
True Sexual Education should also be mandatory in High School, & it should deal with relationships & gender perspectives, not just physical love.
People change careers all the time. To eliminate a core field, when people are so young, will eliminate options when they are older. Besides, who knows what they want to be, at 14, or even 17 yrs old?