I know quite a few homeschooled children through church and my daughter. My daughter, met them in figure skating and public school. The ones in public school had obviously stopped being home schooled. The ones in figure skating were ill equipped to skate, totally unathletic, it was painful to watch. But their mom got all the fees paid, which is outrageous, as I paid through the nose all those years for her lessons, both ice and coaching fees.
She said every child that came into the school from home schooling had terrible social skills. She ended up befriending a young girl whose Mormon parents kept her out of school. But the year they divorced, she fought to go to school. My daughter taught her social skills, but she is still very insecure. She literally has done everything my daughter did, a few years later, including moving cities just to be near here, her only friend. And she is nice and smart. So sad she was not given the opportunity to develop more. Plus, she has no critical thinking skills. She has gotten sucked into the vortex of radical feminism, esp. since Trump got elected, and she has no foundation to evalute whether this philosophy is correct, or if she is comipletely brainwashed, as my daughter feels.
I always remember visiting a family who was home schooling. The daughter was in grade 10 or 11. The father proudly said she was learning fractions, so she could cook, and how well home schooling worked! Try algebra and geometry in those grades. Fractions is elementary school. That really turned me off home schooling.
I do believe parents need to teach their children basics, everything from discipline to house cleaning, yard work, and most important, who God is, how to know and serve him. And yes, some public schools are pretty humanist these days. My son was looking at various kindergarten options for his daughter next year. He figured out quickly that his daughter was not going to learn anything in the local neighbourhood school. The French Immersion was good, but fortunately, she got into the gifted school. Keeping them learning, say math or physics, when you haven't made it through school or post secondary is an exercise in futility. I have loads of university math, but I never would have dreamed of trying to teach my kids to learn advanced concepts like that. So much better to have a teacher with a passion, knowledge and experience teaching those schools.
I was a public school teacher, before I was disabled, and I learned a few things to avoid. Stay away from "open" education and schools with team teaching, and walls moved back. That is just bad news. If you can find a traditional curriculum, that is going to teach basics in the early years, and later, advanced work in real subjects like Literature, Chemistry, Math, and other science, the children will be fine.