What is the role of a parent? Were the parents in the movie caring?

Parents are not really portrayed as especially involved in their children's lives. They drop them off to boarding school and pay a lot of money. Neil's father cares only that Neil follow his academic plan. He seems to live vicariously through his son. Todd Anderson's parents send him the same desk board for his birthday, every year. Mr. Keating inadvertently takes on a parenting and mentorship role for these boys.