First, let me agree with some of your points before I tell you why you are wrong. Children do need to be socialized. They need to know how to interact with others. They need to interact with society. If you homeschool, you need to be acutely aware of this and be certain that your child is getting lots of this. There are many sports teams and hobby clubs out in the world that are a good place to lay this foundation. I also agree that children do need to be taught to be independent, however, public school is not *necessarily* the place where things like that are taught.
Second, I assume you must come from a well to do school district because of your view of the public school. Even the worst parent could put together a better program for their child than the schools in my area. I say that having seen some homeschool disasters, but they pale in comparison to the volume and magnitude of the public school disasters. How dare you paint all those who would homeschool their children as cult wannabes! You would guilt a parent into sending their child to an institution which has a large percentage of drop outs, arrests, and low "achievement" scores just so you can grind your axe against a religious bogeyman?
Third, I believe you are suffering from an observation bias. You see homeschool weirdos. You either confirm they are homeschooled, or assume so, then add that to your pile of evidence. However, you will never add observations of normal well adjusted homeschooled children precisely because they do not stick out! There is no way to avoid this sort of bias without a well designed, well controlled, properly evaluated statistical analysis.
Optimization hinders evolution.