I agree totally with picesmoon. But also:
I think it is somewhat arogant to think that you can provide a better education for a child than teachers who have spent years at university learning how to educate children.
I also think there's a real danger that you can get it wrong, and if you do, there's no-one to notice or to help put it right.
I know two people who were home-educated and they are both some of the most socially awkward people I have ever met in my life. One of them bitterly resents having been home educated, and now that she has her own children she travels half an hour across london every day to ensure they go to a decent school as she feels that actual school is very important.
And it's really not natural for children to spend 24 hours a day with their parents, with parents making all the decisions about their lives, who they are friends with etc. Children should be given the freedom to learn things without the parents being there, and to learn the discipline of having to get up/go out in the morning etc.
Also, I find that HE parents are extremely defensive and closed-minded. There's a real attitude (have noticed it on here) that no-one has the right to an opinion on how your child is educated, and how dare anyone ever question it/want to come into your house etc to see that your child is being educated appropriately.
If parents want to HE then that is obv their choice, but HE should be regulated and there should be some requirement to show that the children are being educated to a certain standard. Because if they're not, then it's still society that has to pick up the pieces.