Earlier quoted context omitted.
I wouldn't trust every teacher to teach well. The simple fact is, there are good teachers and there are bad teachers. Ultimately, it's the parents job to make sure kids are brought up well. That means helping teach during some years and stepping back more in some years. Parent involvement is a must.
Sometimes parents are unable or unwilling to bring up their kids well. What should happen to those kids?
But to answer your unrelated question: Of course, responsible adults, which includes teachers, should help them as well as they can.
Unfortunately, try as they might, only parents can do a parents job. Really, it comes down to providing a good family to as many kids as possible.
Divorce, broken families, single parent homes, foster care, etc... They all fall short of what a good solid Mom/Dad home (with a good relationship between Mom and Dad) can provide a kid. That's where we should be focusing.
Oh, and while I'm at it: World Peace.
*edit - Unfortunately, we can't do anything about people dying or getting sick. But short of that, people really need to be responsible about the situation they are in when they bring kids into the world. And then they need to take care of those kids.