My reply was somewhat different-->
I have never been home schooled myself. I went to a school and I went to regular college and university. I did not even take distance courses. However, I would like to give a couple of examples.
The first time, I ever knew of anyone who was home schooled was when I wen to the home of a major Gujarati poet. [Gujarati is one of the many Indian languages.] This person had two sons and he had not sent them to a formal school and both his sons were quite intelligent and were very well-versed in music and the fine arts. When I spoke about this person to another senior person, he kind-of brushed it off saying it was crazy. This was eleven years ago and in India, where we tend to be conservative, this was quite revolutionary and I believe, successful.
The second example isn't exactly a home schooling one but we had a student who studied in a school, which was known to have a number of issues, including horrible teaching standards and rowdy students. The University where I teach has a unique system, it has a nursery school and then it has a school that teaches students till the secondary level and then they get into the college. So, in the last thirteen years of my teaching there, I have never seen any student who passed out from the school on the campus and was academically brilliant. This girl was academically brilliant. I even asked her and she told me that it was because her mother spent a lot of time on her.
So, even if people say the formal system has benefits, it is clear that children need support at home more than anything else. I don't exactly support the socialization theory because the kid can always learn that from parents and the neighborhood.