Socialist.....
All you need to know to teach someone something, is to know more than them. Since virtually all parents have graduated at least high school, they are qualified to teach to AT LEAST 8th grade.
What you fail to recognize is that most homeschool parents have college educations. And that having a teaching degree does not qualify someone to teach, as is evidenced by the horror stories we hear constantly about teachers.
In addition, you fail to recognize that a one on one education is far superior to a classroom setting and you don't allow for the fact that they parents can learn along with the kids if necessary.
Not to mention that by the time homeschool kids are in high school, they are self-teaching at that point. They have learned to teach themselves and are motivated to do some, something precious few public school kids ever master.
OK please read what I am typing.
My wife is a teacher. She primarily deals with special needs children and the children who are far behind grade level so we have a birds eye view of what is real, true, and factual. The children who are far behind are most often the result of home schooling failures. They are mandated back into the public schools and written off the books on the home schooling organization as if they never existed. What a way to keep a good average.... Most of the parents who teach their kids at home are not college educated. That is a myth.
What you say about high school kids teaching themselves has some truth to it but you have ignored the fact that many of them take a lot of adult supervision to keep them on track. They lack the self discipline to work independently. This is not the fault of the teachers it is the fault of the parents for not teaching them to sit down, shut up, respect others, and pay attention to the teachers. If they can not or will not teach their children these things makes you think they can teach high school math or science?
We are very connected to the UC Calif college system. I don't mean to break your bubble but the kids who do the best in college are not the home schooled kids. The Asian kids who go through the public schools you are putting down far out score and out perform all the rest. What does this indicate? The Asian kids have far more structure, supervision, and much better goals established than their peers. So it is all about parenting not so much about the teachers. There is value in home schooling if the person doing the teaching is qualified and able to teach. There are a lot of teachers out there who have the education but are really crappy teachers. The goal has to remain that our kids get a good education. When you stray from that goal to support your religious beliefs or ego you are making a huge mistake and it is the children who will pay the price. All parents should be able to teach their kids a belief system but few of them can teach chemistry or trig.