I don't need to convince people to homeschool because people in my socioeconomic demographic mostly feel scared that they are not doing it. Most people are not big risk takers, but now, as homeschool grows in popularity, it's hard to tell whether it's more risky to leave kids in school or take kids out.
Pulitzer Prize winner Jared Diamond's most recent book is The World Until Yesterday: What We Can Learn From Traditional Societies. Like so many books, it's an inadvertent argument for taking kids out of school. (Here's another book like that.)
Diamond shows how for most of the existence of humans, a parent, or parent figure, stayed very close to the child until adolescence. In different societies this scene looks a little different – hunting, gathering, building, farming. Parents kept their kids within watching distance, but they did not dictate to their kids how to spend their time.
If you want a tested solution, if you feel that your stomach for risk taking is low, then take you kids out of school, because that's where our society tries child-rearing tactics with relatively little or no history.
But that's so obvious, that the risk avoidance must run deeper. What we are really testing is the idea that parents have built a life that involves their kids. We have separated kids and parents for so long, but if you unlock the kids from schools, and let them all come home, you have at least one parent staying with kids all day long.
We know what homeschooling looks like. There is no risk that it'll be worse than school. We are scared to give up our independent lives to do it. I write post after post about how school is terrible and homeschooling is the way to go. I am much less clear on how it's to be done. I am winging it. And the risk to me is that my kids will get the best childhood but I'll be lost the whole time they're getting it.