Assuming you are Mormon, is home schooling sort of another form of virtue signaling Mormon families employ or is it more of a way to ensure your families don't get excluded? Like, did you really have a choice in the matter once you realized you either go full Mormon or leave the church entirely?
Mormons aren't the only people with large families. Ultra-conservative Jews, Muslims, and many Christians have large families. What I don't think I've ever seen is a couple who is non-religious or atheist and has a large family.
Protestant Christian and most of my Christian brothers and sisters look at how many kids I have and that we homeschool and think I'm a little crazy (just like most non-Christians). I'd say probably 1/3 of the families in our church homeschool though. It's a wonderful community to be a part of and if I sent my remaining kids to public school, I wouldn't be asked to leave.
I'll take the L but it still sorta maps to where I was going with the Mormon angle.
I've been around Mormons, not a religion scholar, but it seems plausible to me the same "one upsmanship" mormons have with missions, large paternalistic families, avoiding "outsiders" (see: homeschooling), etc are common in other religious communities. Like maybe the protestant Christian one you are in?