You are not paying more for a better education necessarily, you are paying more to weed out the trash and increase the chances of meeting a quality mate.
Thus when they start a family they often move out to the suburbs where their children will interact with the fewest possible bad apples in their neighborhood and school. This will help them raise their children to be better adults because what they are trying to teach them will not be undermined on a daily basis by nearly everyone the children interact with.
The parents must pay more for this privilege.
Thus it is with college, but the stakes are higher, because there is a good chance their child will meet their future spouse in college. And everything the parents have done up to that point would all be for naught if their child met some trash from the neighborhood the parents moved away from and married them while attending a state college.
Diminishing the possibility is worth paying extra for.