[Delvo]

Most "home school" programs do have educational professionals running them, designing & approving the lesson plans, and grading the work. When my younger sister decided to leave our public high school, she finished and graduated through such a program. They either sent her the textbooks or told her what books to get and where, they sent her other lesson materials of their own making to go along with the books just like a teacher's own lesson outlines or classroom speech, they told her and our parents which stuff she was supposed to do and when, they answered her questions, and she mailed in her papers for grading. If our parents had not been able to serve her needs or she had not been able to keep up herself, the school administrators would have seen it, our parents would have been unable to hide it or deny it, and action (such as getting her back into a physical school building if that was the better solution) could have been taken to respond to the problem. It's really just school at home, as the name indicates.

What some of you seem to be responding to is something else that's often called "un-schooling" for its lack of formality and structure, and is illegal in some (maybe most) states. There are no lesson plans or textbooks and there's nobody with a degree in education grading the kids' papers anywhere. The kids are generally included in the adult world with their parents so they can see for themselves how the world works and what people do and how they do it and how one piece of knowledge fits to another. The things they need to know just come up in real-life situations because human kids are naturally curious if you don't stifle that, so they come to understand the "lesson" in context of what it's really for because it's a part of how things actually work in their experience with the world around them. For example, by the time my oldest nephew was old enough for kindergarten in conventional schools, he was already doing math that isn't taught there until third or fourth grade, because he had seen how people use numbers for grocery shopping and football games and asked about it. For things that are beyond their parents' normal routines, they find out where else to learn more and learn both the info itself and how to get it, such as looking up written material about it (often resulting in research projects that get turned into displays that they share with other "un-schooled" kids and their families at occasional big gatherings) or going on what normal schools would call a "field trip" (although they do it much more often than schools do it) to see the places and meet the people who really do whatever it is. For example, the last time I visited, we went to a partially rebuilt fort and historic site/park, where they learned some history but also some physics and geometry from seeing how things there were designed for their functions. A blacksmith showed us how people back then had to start fires, and days after I was gone, they were still soaking up more stuff about fire and how people have started, maintained, fought, and used it in different eras and which technologies replaced those functions.

Of course, there's a spectrum of different levels of involvement by educational professionals, and what I've presented here are two extremes: one pretty much completely run as a private school would be except for the physical presence and one with no such people involved in it at all. But it's important not to argue for or against one thing when what you're thinking of is another.