I'm a long way from hunting with my kids. Oldest is only 3.
In NY the law is 12 you can bowhunt or small game hunt accompanied. 14 for firearms big game hunt while accompanied. 16 to hunt unaccompanied. Just FYI.
Anyway, I dont come from a hunting or shooting family. I was the first to own a bow, a gun, to hunt, to camp etc. I've never hunted with my father and that's unfortunate.
Hunting for me is as much about the experience as it is about taking game. I probably won't let me kids hunt unaccompanied until 18 unless I have to because more than one wants to hunt that day and we are all on the same property just different stands. Part of that is the selfishness of wanting to spend as many days afield with them as I can before I'm too old, they move away, go to college, get on the 9-5 grind, get married etc. They will all likely have many more hunting days after I'm gone than they will while I'm still around.
Lastly, it depends what kind of hunting we are talking about.
Sitting in a stand a couple hundred yards from me? Yeah maybe at 16. But probably not all at once, first I will walk out with them and then go to my spot, then eventually they can do it all alone.
Tracking in the Adirondack wilderness where you can't see 100yds and you can walk all day without hitting a road? Not a chance in hell I'd let them go alone until 18 and that's assuming by then they have demonstrated maturity, woodsmanship, navigational skills, and sufficient physical ability.
Just my .02
