I expect that any reasonable high school graduate could teach any or all of these subjects. There are lots of curricula available.
It amounts basically to intensive, year-long tutoring by someone extremely familiar with the student, extremely committed to the success of the student, and with an automatic hand on discipline.
On average, home-schooled children do better than those in public education across the board. Shall I dig up some cites?
The socialization thing is nothing. Check any private school in the area. Ours has an extensive program to include any home-schooled student in sports, drama, speech contests, and so on. In some states, public schools are required by law to accept home schooled children into their intra-mural programs. I have heard horror stories of public school administrators who denied this.
One con of home schooling is that the public school system hates it with a passion. You don’t want to know the things I have had said to me by public school administrators who thought my kids were being home schooled.
Regards,
Shodan