Almost universally students with more active parents do much, much better. It's not a chicken and egg argument, it's egg--that's it. Even in a terrible school, a parent with modern technology has more than enough resources to give their kids a huge boost. Hell, just reading to children has a large correlation to doing much, much better in school. Parents who give a shit, and have the time to nurture and help, can push any average child to at least a level where college and stability are fairly easily obtainable--regardless of how terrible their school is (Barring it being a war zone or some other extreme outliar.)
This, not the schools, is the primary difference. Now, this doesn't mean some schools don't have advantages, they do. Teachers which aren't frustrated or apathetic will teach better. But again, the thing is, at that point, where the schools REALLY matter? You're starting to divide people already above the average spectrum, so everyone in those groups should have a decent shot at being successful (In other words, parental involvement, even with a bad school, is good enough to do well, after that point a good school can push someone to do great; but the issue is many kids in 'bad schools' aren't even doing well, and that's not the disparity in the schools causing that.)
If we focus on schools, it would be like stitching the skin above a severed artery--we aren't addressing the problem, at all. We're dealing with a symptom. No school can replace a parent, no teacher will have more of an effect on a kid than an encouraging parent who is involved in their education. The question really is, how do we get poor families to the point where they have the stability and self sufficiency to offer this to their kids? How do we fix the chronic problems in these communities? That's a much more complex answer, and so people focus on the schools. Because it's an insitution we, as voters/government have a clear cut amount of power to change things in.
But we're deluded if we believe we believe we can exert as much influence in 900-1000 hours a year, as children get influences in the remaining 7500ish hours at home. 11% of the time? No, sorry. You're never going to be a good enough school or supervisor to alter bad behavior or help someone when you only occupy them for 11% of their time, and they get the bad behavior reinforced for the other 90% (Or however much after sleep).