I'm pretty religious right myself, honestly. I have nothing against homeschooling and am a Christian. It's the quiverfull movement I'm talking about, which does teach that the man is the head of the house hold, and he's the only one that can communicate directly with God, all other members of the household can only please God by obeying the man of the house. And yes, you need to have lots of children, because any birth control at all, even natural family planning, is as bad as having an abortion, and you need lots of children to penetrate to world with your beliefs (this is where the term quiverfull comes from, the children are arrows in your quiver being shot into an unbelieving world).
An interesting read about this extremism and how it's really abusive:
Vyckie Garrison on escaping "Quiverfull."
I'm not sure how "pure" of a form of this the Duggars are practicing, but from what I've seen of the show, this does describe them.