I'm now a secondary school teacher, but before that, when my son was 7, over 25 years ago, I withdrew him from school and home educated him for a year. School was totally failing him and I was worried for both his physical and mental health. We went to museums, art galleries, lots of farms, did reading and writing and some maths, spent a lot of time in the library, on the allotment and learning how to swim. But, my son has a life limiting and life threatening condition.
I believe a lot of what's been described in the earlier posts isn't home schooling, instead it's a mix of online learning and private tutoring, a bit like an informal 'governess' approach and the 'home' part of it simply describes the location rather than the type of learning or the content.
What's clear is that schools aren't for everyone. They appear as a mass phenomenon from about 1870 onwards and replicate the environment of a factory (and yes, these days the factory is more likely the office). It's unsurprising that those unsuited to the factory model can't thrive at school.
What really needs to happen is that we should have a conversation, as a society, about how children learn and how we fund that. I don't know the exact figures, but it's something like £6k for secondary kids per year - that's to cover staff salaries, all bills from the school environment, equipment (including textbooks, exercise books, stationery, sports, etc.) and so on. Roughly speaking £150 per week. If you consider a private tutor is £50ph (for a cheap one) and you probably need 4 (maths, English, science and a humanities subject), then you're already spending £50+ a week more than state secondary. Once you add in online learning materials, textbooks and stationery, you're at another £50+ per week. You get the picture. It shouldn't come as a surprise to anyone that doubling the funding for education per child (once you add in everything else) results in better outcomes, particularly in terms of their capacity to cope, because they're getting so much more support.
But the question we really have to ask ourselves, as tax payers: should the resources be more evenly distributed for the benefit of all?