Homeschooling is, in the majority of cases, a bad thing insofar as it serves to shelter children and, all too often, spoon-feed them religious and political dogma rather than actual knowledge about the world. I share this trepidation with DemPGH, and wish to see it discouraged, stigmatized, and tightly-regulated.
What cultural richness do you imagine children discover in public school? Children form their own social monocultures, devoid of reason and impervious to outside influence, which is the genesis of the problems you describe. Students indulge themselves in group think and perverse cultural norms that stop them from learning. The public school system is the absence of culture and reason.
Homeschooling is vastly superior by comparison, which is a commentary on the ineptitude of school administrators and government policy wonks, not an endorsement of homeschooling.