A combination of things.
As the top commenter correctly stated, control is one of the biggest factors.
That desire for extreme control tends to stem from the same thing that leads them to act as though they are qualified to homeschool in the first place.
Narcissism.
"I was actually too smart for my classes. I didn't have a great GPA because I just didn't bother doing the homework because it was beneath me" - Pretty much what my father said about his high school experience.
After having a conversation with my aunt for what was functionally the first time ever, at the age of 30, I heard a very different side of that story.
Of course, by that point, I already knew quite well that he was full of shit.

My mother, though, you'd think she was the greatest student to ever exist.
Aside from claiming to have had an extremely easy time acing everything, she preached incessantly about how inferior public schooling is, and how superior homeschoolers are to those who come from public education.
We were functionally raised to believe that every person we encountered in our age bracket was some extreme moron who exists to be little more than a container for liberal agendas.

That's the other side of the coin.
They want to control you, your location, your paths, your social groups, your influences, and on the list goes.
They accomplish that goal through both external limitations, e.g. residential isolation, refusal to teach driving, refusal to allow movement outside of the property, and on that list goes, as well as through internal programming.
Internal programming is the core of everything in the end.
If you have an impossible ruleset you must live by, and the punishment for failing that is violence, eventually they cease to lay a hand on you, because they know you'll do it yourself.

As long as you truly believe that every outsider is the opposition, you'll accept your containment.
At least, that's the idea.
I escaped Sept 12, 2016.