The hard sciences should absolutely be compulsory in HS. The hard sciences of biology, geology, chemistry, physics, mathematics, and others should at the very least be briefly discussed in high school. Even if a student has no interest in pursuing a career in science or math, they should be exposed to these hard sciences, simply for the educational value of these subjects. Imagine how poorly our high school graduates would perform if they had no mathematic or scientific knowledge beyond the middle school levels. It would be disastrous.
At least some science should be mandatory. There are kids who will grow up and do wonderfully at a science career who would've never considered it if they never had to take a science class.
The advancement of science helps everybody. While it is true that not all kids will go into science if science isn't mandatory then less kids will.
If we are only taught what we need or want to know, then the American Public Education system would need to be completley re-designed. Very few people take genuine interest in the hard sciences. It's not till they have learned the applications to the world that the hard sciences have that they become interested. The socioeconomic classes would also have much larger gaps.
I got the idea of this opinions question because Cowboy told me that the sciences are compulsory in the US.
Some kids may want to pursue a scientific career, such as medicine, in the future. These students should certainly be able to to scientific subjects like physics, chemistry and biology for them to pursue their future careers. Other students might want to take these subjects purely out of interest, and that's great for them too.
However, it is unfair for the hard sciences to be compulsory because different kids have different abilities. Many of them do not have a gift for memorising meaningless Greek words or calculating complex mathematical problems required by physics. Teaching sciences at the secondary level will only reduce their interest level in the discipline.
Also, the sciences serve little practical purpose for students who do not intend to pursue a related career, and we're wasting their time by making them learn stuff they'll never use. You don't have to know how radios work to listen to the radio.