Newsflash: the relationship between individuals and society is much more complicated, and has very little to do with the expression "for the sake of". (imho) That expression implies to me a "guiding purpose" for one side or the other of that relationship. I think the evidence for a cognitive guiding purpose, especially one that understands what is good for individuals, or the common good, is .... weak.
I think the original Slate article did not make the point explicit, but if you'll grant me that parents want to do something for the benefit of their children (not that it is their *duty* any more than it is society's *duty*, but empirical evidence suggests it is a compelling motivation)....
If you grant me that, I think the point can be made that improving the society a child (and that child's child) enters is very much in their best interest. A country with fewer foreign wars, less domestic crime and terrorism, better governance, and (dare I say it?)* higher levels of social justice and economic equality is MUCH MORE IMPORTANT than an extra 5 points on the SAT. (or whatever)
And I think the strategy of supporting public schools is in line with that achieving those goals, even if it takes some of your time, energy, or money away from other things that benefit your child.
I'm trying to stay away from the strident, accusatory tone of the Slate article. It seems to have put your teeth on edge, and I'm sorry for that. I can see why it is completely unconvincing to someone who who rather read corny rebuttals than admit that you might care about more than your own children. (Don't you care about your grandchildren? Neighbors? Do you really think the Louis CK thing and say, I don't care what you do with your f'ing kid?**).
If you do care about your kids, take some time to consider how to make collective agreements with the other people in the world, in your country, state, county or municipality, and even in your local public school district. Making those collective agreements improves that irritating 'society' whose altar you seem so outraged by. Because I really think that if too many people completely ignore it, eventually the collective is going to start doing things that are bad for your kid. I don't have any facts at hand.... it's just a feeling.... but I'm convinced of it. Maybe you've already noticed some evidence?
How you react to that prediction (i.e. with engagement vs disengagement) says a lot about you. I personally choose to support engagement. But, as far as personal liberty goes, I recognize it as a choice.
Last link***, to help you empathize with the people who hold opposing viewpoints: I think this is not a red/blue policy distinction, rather a 'inherited obligation'(red) versus the 'negotiated obligation'(blue). You're explicit that a parent doesn't have a duty (for one thing) but I think you imply that there is another (fixed) duty instead. If I interpreted you correctly, that makes you an 'inherited obligation' thinker. The link (in footnotes) is there to allow you to see the other way (negotiated obligation) as a valid personal choice, held by decent people you'd be happy to call neighbors or friends. Even if you never come to view the world that way yourself.
* I have a source for that, though it is weak, I'll admit. Economic equality is the subject of my favorite TED talk, with facts and figures. But it doesn't make the case that equality is better than statistically meaningless differentiations on standardized college admissions tests. Only that by itself, it brings better health, longer life, higher literacy, higher levels of societal trust, lower crimes, lower mental health issues, and a raft of other improvements to societal statistics. But not necessarily for *your* kid, so yeah.
** "Like when you see someone stand up on a talk show and say 'How am I supposed to explain to my child that two men are getting married?' I dunno, it's your shitty kid, you fuckin' tell 'em. Why is that anyone else's problem? Two guys are in LOVE but they can't get married because YOU don't want to talk to your ugly child for five fuckin' minutes?" – comedian Louis CK on gay marriage. (editorial note: maybe it's funny, but also a completely counterproductive liberal asshat thing to say.)
*** http://www.gurus.org/dougdeb/politics/209.html "Red Family, Blue Family: Making sense of the values issue"