As someone who was homeschooled, I mostly agree with the Beauty Parlor gals. I think homeschooling is very often bad for kids because it heavily relies on the parents. You can either be born with math teachers for parents and go to Harvard like those child geniuses, or you can have neglectful parents that don't bother to teach you anything. In my case, I wasn't taught past the first or second grade; I never learned math beyond 2 plus 2, and I was never taught proper grammar or history. My mom would never pass a teacher's exam. Not to mention, I was constantly isolated beyond the one homeschool group I did. I never played organized sports or had any social opportunities like making new friends and hanging out at people's houses, and I never got the freedom and independence almost every other kid my age had; I basically missed out on my entire childhood, and now I don't even have a driver's license or any way to escape my mom. I'm completely miserable, and homeschooling enabled my mom's neglect.
In public school, everybody gets the same opportunities. Sure, it's not perfect; you have the famed "wokeness" in schools and teachers raping kids and every other issue people bring up with school, like bullying, and while it has its issues, I think it's still good for kids because, for one thing, kids learn to overcome their struggles and do things they don't want to do, like waking up early and sticking to a schedule, but also because a kid from an abusive family can get an education. Make friends and move away to college, mostly prepared for the real world and not be completely sheltered from it If they went to public school vs. homeschool, that same kid might not even learn how to read, not to mention the fact that Parents need to make an extra effort to make sure their kids are socialized and not completely isolated. If my parents didn't sign me up for that youth group when I was a kid, I would have literally never talked to anybody except my family, and even then most of my friendships didn't last.
I would also like to add that most homeschool stats like the one Op cited suffer from convenience sampling, which means only the successful families submit their tests, so you don't see the poor test scores from unschooled van-life kids as opposed to public school, where every score is submitted, meaning failing students are documented. So this creates the false perception that homeschool kids are far ahead of public school kids and that everybody who homeschools is better off. Who cares if you ignore all the examples of kids being abused and neglected with no legal recourse that are well documented? Heck, it's legal to not teach your kid how to read or the ABCs as long as you say it's homeschooling. To say that everybody who homeschools is better off is a flat-out lie. Just because you had a bad experience in public school doesn't mean homeschool is sunshine and rainbows, and yes, I do concede that successful homeschool happens, but far too often homeschool parents neglect their kids' education, and we have no laws in place that could prevent bad homeschool parents from abusing their kids as opposed to public school kids having trusted guardians who can call CPS if kids are abused.
TLDR: Homeschooling is bad in most cases. Send your kid to a public or private school instead.