The rebuttal to your point is so simple and obvious it's really hard to take you seriously. Socializing is a skill that can be practiced. If you have fewer opportunities to practice, you're less likely to get better. The children that are bad at socializing despite going to public school do not show that public school doesn't teach socializing, it means they didn't learn as much from their practice. For all you know, poorly-socialized public school children would have otherwise ended up living in their parents' basements until 45 or turned into serial killers if they were homeschooled. Public schooling doesn't need to guarantee good outcomes to be the more desirable choice.