One of the biggest arguments against homeschooling that I've heard is the "socialization" argument. This assumes that homeschoolers never take their children outside or allow them to play with other children. What's worse is that some people seem to think that a child can only be properly socialized correctly if a child is sitting in a classroom. There is a belief that the commonality of experience will eventually be the primary social glue when our children become adults.
Homeschoolers simply shake their heads at this. Most of them bring their children with them on various errands, they involve their children in play groups, homeschool cooperatives will often have "classes" where the kids get together to study, and many of these children are involved in sports and community activities (like boy scouts). They view learning socialization in school as being one step above learning socialization in prison.
I lean toward the view that schools are not a good place to learn socialization.
Unfortunately for my older son, neither situation has worked terribly well for us. At home, he was lonely during the day. Our attempts to get involved with things like scouts, sports, and lessons very often did not go well. We had the best run of luck with scouts, but my son often saw the badge-earning activities as being a waste of time. He always participated fully at events, but he was seldom interested in earning badges outside of the meetings. Without badges, you can't advance. Unfortunately, the scouting system is tied in so closely to schools that there really is no such thing as individual advancement.
Public and private school have been nothing short of a nightmare. My son easily is overwhelmed by sensory issues in large groups, and his behavior falls apart when he is overstimulated. He has managed to make a couple friends, and his ability to control his behavior has improved with time. Unfortunately, he has not found many people who share his love of reading. In fact, he complains almost daily that he hears people talking about how reading is stupid.
Many gifted specialists discuss grade acceleration or skipping. Because of my son's learning disabilities and difficulties, our efforts to do something similar in our schools have been unsuccessful. We live in a town that is big enough to have options such as public versus private school, but it is not big enough to have a good set of special programs set aside for the gifted.
My conclusion is that there is just no good way to socialize a child with my son's unique (in my town) set of giftedness and learning disabilities. I have been told that there are programs in bigger cities that might accomodate such a child. I have hoped until now that we would be able to find a working option for my son, but I am now seriously considering moving to a bigger city.