I haven't watched the video yet, (nor do I have time to anytime soon) but as a former homeschooled kid who grew up and sent her kid to public school this is my experience/guess:
1, Homeschooled kids do better in college
2, Public school parents don't love their kids as much (this is implied rather than outright said, but implied heavily and often)
3, "They'll indoctrinate yer kids! They'll turn them gay/socialist/satanic!"
TLDW: Lie 1. Physically abusing your kids is a proper form of discipline. Lie 2. Questioning the existence of god is the result of trauma. Lie 3. Public schools are anti-christian bastions of immorality.
I don't know man. This is a weird video, and lies 1 and 2 seem irrelevant to choosing public vs. home schooling.