You are probably right as to reading, writing, English, geography, social studies, and foreign languages, but do you really think that most parents are able to teach math and the hard sciences beyond the most basic level? I'm not talking about simple algebra, geometry, and earth science, but rather, linear algebra, calculus I and II, advanced statistics, chemistry, and physics, at the 11th and 12th grade level. Even if a parent knows the course material backwards and forwards, they may not be able to teach it, and even if they are good teachers, they may not have sufficient knowledge of the subject matter.
That's what community college is for!
Well, calculus and statistics are college level courses that many people going into college don't need.
If a high school aged kid really wanted to take calculus or statistics, they could take it at a local junior college.
I would imagine they could do the same with chemistry and physics.
I know I could teach all of those courses except physics, and my husband could teach physics.
Many high schools don't even teach calculus. That is usually only taught in the city high schools.