I think the point is that part of having a functioning society (civic life, engagement, tolerance of others) is having people mix together. School is one of the prime places where that happens.
If you allow a lot of people to pull away from that "forced" engagement with others then you start to stress a lot of societal bonds.
I don't know a single homeschooler that sits at home all day long. They work in family businesses, participate in bands, sports, and co-ops. Many belong to churches where families come from all different strata: our church has surgeons, line cooks, programmers, self-employed handymen, disabled vets. They interact with everyone—including kids. They do things like "kid markets" where they have a business. They watch their parents learn how the house works and how to manage finances.
There is no forced engagement—in fact the peer pressure is often completely gone. They are in an environment (their family) where they are much freer to be themselves.
The best functioning society that I experienced was when 90% of the people were (presbyterian) Christians. We replaced that with something very, very disfunctional.
If you allow a lot of people to pull away from that "forced" engagement with others then you start to stress a lot of societal bonds.