Adding a child into this mix is a whole different conversation. I was speaking mainly from the precision BR, LRS, point of view. For hunting down here and my kids.
They were shooting my hunting rifles at the ages of 6, 7,. Before I ever took them hunting, and that depended on what kind of hunting trip we were taking and the focus on were they going to make the kill shot.
To make a long stories short for hunting down here in the south back in that time when my kids were kids, We always hunted with my 30.06 for me and for them I took my win. 3030. Which both of them have shot 100 times before I ever put the gun in their hands at 10 or 11 on a planned hunt. The point I'm trying to make is. For their age, experience , and size. They had a gun that fit their ergonomic stature. There is a world of differentence in my hunting and my target rifles. You as their Dad will have to make that call. You know your kids and their capabilities better than anyone. The right size gun for a persons build is always best.
Just train him with the best fitting gun you have in your arsenal. If it looks promising and he can handle it. Go for it. But train him first with it before you take him hunting.
This post just brought back memories of the first time I shot my dads 30 plus inch over and under goose gun at 7yrs old. You can imagine the outcome.. As for my buddies on a planned hunt. We discuss what each one is taking so all equipment is counted fore, before we leave the house. And hopefully he picked the correct weapon for his use. If not he will have to make due with what Is available. The smallest gun I take with me on all hunts and fishing trips is ,, My old trusty 10mm. Heck, I got to where I'm at,, by shooting all different size guns. Some bigger than me.
That just taught me that,, some guns work better me,, but I will still jump on the big ones. Lol.