I'm both a teacher and have (at various points) home-schooled my kids - one for a year when he was eight and another for two blocks of three months when she was a teenager. In each case it was to do with mental health. Neither became school refusers (that's what I was aiming to avoid).
One of the issues with home schooling is that there's no oversight. You can pull your kids out of school and no one is going to check up on you. This is a really big safeguarding issue, particularly in deprived communities where parents / carers take the decision to home-school because they can't be bothered to get up in the morning, wash the uniform, make sure little Johnny has what they need, etc. Essentially, everyone knows that in some circumstances 'home-schooling' is code for legalised neglect. The government, via the DfE, needs to introduce statutory frameworks to protect these children's right to an education. Because this is what we're talking about: education is a human right (as defined in human rights legislation).
Secondly, yes there are problems in the education system and wider society, huge problems, but the solution isn't always home education. What actually happens when a child is home educated is that they become isolated (doesn't matter how many activities you do with them) from the rest of the world because the rest of the world is operating according to certain norms of behaviour. People might not like these ordinary ways of doing things that we all learn after 11 years in education, that's fine, they might want little Johnny to forge ahead on his own path, but 90% of the people and systems he's going to come into contact with in his adult life have all been moulded by this 11 years. In other words, to draw on Freud, John the man is going to find himself feeling less at home in the world. What other people have internalised and naturalised is going to be unfamiliar to him. And while home education might have instilled certain strengths in him, he's still going to be a stranger in a strange land and he'll have to learn to navigate that.
Finally, and I think this is my biggest bugbear, I don't think most people have the knowledge to be able to deliver learning. I teach humanities. Very very occasionally I might cover a physics class. I've got a GCSE in physics, but I literally don't have the expertise that a degree and a masters confers. Christonabike, I even once covered a carpentry class. I can put up shelves, but I can't do dovetails. Sure, home educating parents can cover the spec to get their kids through the exams, but that's not the same as actually educating children. Instead, it's feeding information into a system (like a Chatgpt prompt) to get it to spit out a result. In other words, it's creating the very conditions that they're supposedly trying to escape from, i.e. treating people as cogs in machines. To that extent, it highlights a flawed logic at best, and a complete misunderstanding at the other end of the extreme.
All that said, I do believe huge numbers of parents are home educating to try and cope with a horrific increase in childhoodo and adolscent mental health crises. Fundamentally, this is what I think needs to be addressed with more support both inside and outside of school.