I've been thinking about this a lot and am so glad I wasn't in this situation during my schooldays - or that I'm not a child now. My parents were not academic at all, whereas I loved school and learning. I would get moaned at for doing too much homework rather than helping around the house. I was also really interest in, and good at, English (reading, creative writing etc) and languages along with geography and history but in my dad's eyes, the only type of schoolwork that counted (no pun intended) was maths or, rather, mental arithmetic. He would be furious at the amount of time I spent reading or learning useless subjects and would give me maths test every evening which would inevitably turn into screaming matches between us when I couldn't do it. So I can't imagine how awful a home schooling situation would be.
My parents were, and still are, completely opposed to technology too. I was not allowed a calculator to help with maths, despite me telling them that they were actually pushing me further behind by not allowing me to learn maths in the way set by the curriculum and they refused to allow any type of computer in the home.
I moved back home for my final year of uni and it was a disaster. My mum actually threw my laptop on the ground to try to break it and kept hiding all my books and notes, threatening to destroy them because I was being so boring and swotty, studying all day. I was trying to write my dissertation and almost had a mental breakdown.
Home schooling would have destroyed my future academic career and I can only hope that the school would have recognised the problem and intervened.