Isn't it terribly arrogant of people to impose their own faith (or lack thereof) on their children?

Parents teach their children as best they can. When the children reach adulthood they are capable of making their own decisions on this front. God gave us all brains. As parents we do our best to teach our children how to use them. Some people get upset when their children exercise their free will. I actually enjoy seeing it. It means we as parents have done our job. If we are good at listening, we can often learn a lot from our children.