I got really into fencing as a kid, which for whatever reason attracted a lot of private school and homeschooled kids, so I got to interact with the whole spectrum. I'm in an affluent, highly secular area, so this was basically the best case scenario for those homeschooled, and they were still definitely weird.

No amount of artificially constructed socialization immersion is going to beat the organic development of spending several hours, every day, surrounded by a ton of other kids.

What you end up with is a kid who has marginal experience with conflict resolution, communication skills, and any degree of independence. Which in turn, makes them perceived as weird, meaning that when they do have social interactions with others, they get marginalized, and further deprived of social development.

Public schools definitely have a misalignment of interests problem, but private schools solve that problem without stunting your child's charisma.