"I'm going to digest this rather than quoting it: It's the straighforward proposition that if the state compels you to put your child in a horrible school, you will have skin in the game, an investment in the system, and then will in turn forced to vote the way the Teachers Unions want you to, and this will make Skoolz Better, or something.
Although she does specifically say she doesn't want to ban schools; she just wants to make the moral case why you're horrible if you attempt to educate your children....
I'm omitting something here. You can check the article for her exact words. She sneers off the idea of religious reasons outright, but then says wanting your kid to go to a school which is not horrible is a worthy impulse in and of itself, but that's all the more reason to send your kid to a horrible school.
Here it comes. Here's the part where she starts saying -- and she really does say this; I won't be paraphrasing, but quoting -- that she went to terrible public schools and learned (by her accounting) almost nothing, which is precisely why all kids must be forced to go to public school."
Saddly, I've seen this argument mad before by real live people, and not just the leftbots who propagandize for Slate/Gawker/MSNBC.