This appears to be another of those broad, sweeping, statements made by groups with an axe to grind. Doesn't whether you send your kids to public school, private school, or home school them depend a lot on circumstances?
What schools are available to the child? What can the parents afford? What is the child like? My grandson has public school available to him. He has two different private schools available. Home schooling is a possibility, since my wife (his grandmother) was a public school teacher, then got a doctorate in teaching teachers to teach (!). There are other home schoolers around, which means some swapping of things is possible.
But our daughter choose to put him in public school. Why? He is an extremely social creature, and needs the time with other kids his own age. That probably has a severe impact on the success of home schooling him. The local public schools are clean, and the teachers appear to treat the students with respect. They seem to have a genuine concern for the students' success. Frankly, we can't afford either of the private schools.
A number of years ago, our two kids went through a mixture of private schooling, home schooling, and public schooling. The circumstances and the kids were different.
Before we totally slam public schooling, private schooling, or home schooling, let's carefully consider what is availabe in that area, and what the kid(s) is/are like.