It's quite a myth that the "vast majority" of people "cannot" homeschool.
The most convincing story I ever read was right here on FR. A grandma volunteered in her granddaughter's 3rd grade class. One week the teacher asked grandma to teach remedial reading to a couple of students. Grandma protested that she didn't know how to teach reading. The teacher replied, oh, every page has instructions you can read on what the child should do. Just guide the student through that and you'll do fine. After grandma taught those kids to read in a few weeks, she decided to homeschool her grandchildren.
Anyone who can read and write at a passable level can homeschool.
The parents' failings, for lack of a better word, can have the same effect whether or not the child is homeschooled. For example, I know two families where the parents regularly use poor grammar ("we don't have none" etc.) In one family, the children go to public school and are taught correct grammar. In the other family, the children go to homeschool and are taught, by virtue of the language arts books they use, correct grammar. All the parents still say "we don't have none," but the public-schooled children also say "we don't have none," regardless of what they have been taught in school, and the homeschooled children say "we don't have any" b/c they go on what their books say is correct.
I'll bet Grannie could have just waltzed into the Advanced Physics class at the local high school and run those kids thru
the calculus used there too.
Come on, get serious, there is nothing required to teach reading to third graders but a love of children, patience and persistence. Reading should be fun and is not hard to make it so.
Your examples are hardly convincing arguments against my statements.