I guess I'm in the minority, in that just about every family I know homeschools their kids, and the homeschooled kids have LOTS of peers.
I suppose there are lonely homeschooled kids....
I'm a member of Sovereign Grace Church in Chesapeake, Virginia, and while the pastors have made it clear that homeschooling is absolutely not "the only way to educate your children," most parents (probably over 80 percent) in fact *are* homeschooling their kids. There's a nice homeschooling enrichment program at our church, field trips that kids can do with each other, more advanced classes taught by members of our church, and a community college that accepts high school-aged homeschoolers. The kids I know who are homeschooled are VERY well socialized, and have lots of friends.
Again, perhaps the non-loneliness of homeschooling that I witness here is the exception....
I think where you live and the type of community you live in does have an effect, but I think the socialization factor in general is becoming less of an issue as the movement grows. New homeschooling networks like at your church are forming in towns all across the country.
Today's 6-year-old homeschoolers should be less lonely than their older counterparts.