Thank you for asking, Radarmark. The subject is complex, but, generally speaking, to me it seems a choice between Scylla and Charybdis. I don't see that children educated, or, perhaps more accurately put, socially engineered, in public schools fare much better. Catholics, if at times arguably alarmist, are at other times trenchant critics of the Marxist left (as well they should be, given the respective histories of both), especially, in this case, of the influential Frankfurt School, and this, it seems to me, is worth considering as a case in point:
Source (p. 83):
Patrick Buchanan:
"Another of the insights of Horkheimer and Adorno was to realize that the road to cultural hegemony was through psychological conditioning, not philosophical argument. America's children could be conditioned at school to reject their parents' social and moral beliefs as racist, sexist, and homophobic, and conditioned to embrace a new morality. Though the Frankfurt School remains unfamiliar to most Americans, its ideas were well-known at the teachers' colleges back in the 1940's and 1950's.
The school openly stated that whether children learned facts or skills at school was less important than that they graduate conditioned to display the correct attitudes. When Allan Bloom wrote in The Closing of the American Mind that "American high school graduates are among the most sensitive illiterates in the world," with some of the lowest test scores on earth in comparative exams, but the highest scores for sensitivity to issues like the environment, Bloom was testifying to the success of the Frankfurt School. Parents may consider today's public schools costly failures where children no longer learn. To the Frankfurt School, they are a success; for the children coming out of them exhibit all the right attitudes ..."
I think, then, and often, the parents who educate their children at home are reactionary and consider themselves largely forced to, in order to counteract this "attitudinal" trend and to reverse engineer, or engineer reversely. Furthermore, they see themselves as essentially compelled to respond when the attitudinal trend is analyzed within the context of an anti-Christian history, with avowedly anti-Christian goals, coupled with Marx's statement, in The Communist Manifesto, that children, in the utopia he envisioned, would be freely educated in what he called "government" but which many of those Christian parents call "public" schools. Parents, and not just Christians, are increasingly opting out. And if some of those parents create a few neo-Luddites in the process, well, then, so be it. Who knows? Perhaps a new Amish culture, of sorts, is in the making.
Serv
No one would be left. 
