Homeschooling will certainly produce some socially awkward adults, but the odds are good they would have been just as quirky had they spent twelve years raising their hand for permission to go to the bathroom.
All the homeschooling parents I know meet on a regular basis with other families. They organize field trips, cooking classes, reading clubs and Scout troops. Their children tend to be happy, confident and socially engaged.
The process of socialization is nowhere near complete at age five or six, when modern children start spending up to half their waking hours taking their cues from other people’s children. Because they accompany their parents’ daily routine, homeschooled kids spend plenty of time interacting with people of all ages, which I think most people would agree is a far more natural, organic way to socialize.
Most of the homeschooled children I know have about the same amount of after-school peer time as the rest of the population but, obviously, without that school day together, they do spend less time with their peers. Whether that’s a good thing or a bad thing is still open to debate.