I'm glad a few weeks ago I could take my youngest son (10) hunting with me for a memory of a lifetime. I think the key is that the child is supervised. My 12 year old son has shot three bucks.
One problem of exposing children to hunting at 16 or so is that you might have to much competition at that age. Girls and cars. There is a fascination in a boys eyes at a early age that might not be there later. I'm really not a big hunter. I have never shot at a deer myself.
One thing that helped us was being at a club that provided guidelines. I would have felt very uncomfortable on public land or at a club without a board to check in at before the hunt. We hunt out of box stands which allow for great conversation and mentoring/relational parenting.
I really wish this were left open for the parents who want to invest the time to do it right. There is nothing like walking up to a buck with your son and saying "Son, you have what it takes!" Those are the words every young boy wants to hear from his dad.