This question arose from my hub "Why I am Considering Homeschooling my Child"
I think this would be an excellent title for someone to write a hub about - I would have to research it more before writing a hub about it, so I'm not going to tackle it in the near future.
From my limited experience while considering this option for my child with Asperger's Syndrome, I would say that a lot of bullied children are homeschool. Thye are bully magnets (their peers find them "weird" or socially awkward) and are not coping with mainstream school. I read on forums many homeschooled children thrive. Also many parents said it is very hard on the parent, and not everyone can do it. My child is socially awkward and unusual (many would say weird) because of his AS.
I also know of people that homeschool their children for religious reasons - I often wonder if an attempt to shelter their children from other beliefs (in some cases, I imagine parents can make their child weird/socially awkward).
A school principal told me that he wasn't a fan of homeschooling because he thinks "regilious nuts do it and don't teach curriculum only religion = neglect". Another said he wasn't a fan "because not enough social interaction". These are the usual stereotypes cited against homeschooling.
Homeschoolers need to make effort to have social opportunities for their children, not isolate their children.
Some homeschool because of illnesses like chronic fatigue. Others because their children are bored in school, because they are too bright for mainstream school. It all depends on personal situation whether it works or not.
Gosh, I've nearly written a hub about it!