I grew up in a day and time when home schooling was not a common alternative for public or private schools. Some of my friends went to smaller Catholic schools, and a select few attended "experimental" private schools with a more casual approach to education. The rest of us, however, had to attend public schools from grades K-12.
My graduating class had 512 members, and the entire 9-12 class population was around 2,000 or so. That's a lot of friends, enemies, bullies, drug users, jocks, brainiacs, band members, shop kids and drop-outs for one teenager to encounter.
Had I known it was possible to learn everything I needed to learn from elementary, middle and high school at home, I would have jumped at the chance to enroll in home schooling. Socialization skills are important, no doubt, but in my own experience, the biggest lessons I learned from other students were to keep my head down, hand over the lunch money, don't make waves and avoid the oddballs at lunch or recess.
I think the major problem with home schooling at that time was finding parents or tutors who had the time and expertise to perform like trained educators. It would have been a challenge to stay inside and study math or science while a perfectly good backyard was only a few yards away. Modern home schooling seems to be much more organized, with support groups for teachers and ways for students to work together on projects or to work on socialization skills.
I don't believe home schooling is suitable for every type of child. Some children would probably benefit from the discipline and structure of public schools, while others would be better off not having to deal with the bullying and social ostracism often present in large groups of children.