Kids are a part of society, and society has a stake in what kind of adult they become.
In the same way drug addicts are society's problem, or unemployed people are society's problem, or sociopathic second generation rich never-worked-a-day drunk drivers are society's problem.
This isn't to say that you'll be conscripted in to a psudo-parent role against your will, but they are your responsibility as a member of society in a very abstract way.
