OldTurtle you are right on here!
First off my kids don't NEED anything. They could hunt with the Rossi 243 we have for years to come and do just fine, well maybe, but I am growing tiered of buying "entry level" equipment for them, only to have to upgrade due to poor performance or them outgrowing stuff too quickly. In the last few years I have had to replace/ upgrade more than I can remember. Let me think, "kids" fishing rods and reels, a single shot 410, a cricket 22 rifle, two kids bows ( $100 pos that broke)cheap binoculars, cheap Kmart camo clothing and coats ( cold boys have no fun), cheap hiking boots (kids with blister have no fun), cheap rifle scopes, cheap snowboards and skateboards, entry level metal detectors and pin pointers, and on and on. I know I would be money ahead if I had just spent the extra money upfront for good equipment for them in the first place, plus learning might have been improved and I would have had to deal with less problems.
When my I turned 12 and was legal to hunt my dad gave me a beretta AL3 shotgun, that was 29 years ago and I still hunt with it. No, my boys don't need an AR, but I know me, and them, and it will not be too long before we will want a little better equipment. In time I know they will want one because I hunt with ARs anyways.
I will say the Rossi Trifecta has been a good little gun, I probably have the only "good one" they made and my son does not want to sale it.
Other benefits to an AR for my boys and me are, first I already have a lot of parts from my own builds, so I'm already ahead $ wise. Next, a sliding C.A.R. Stock is faster and cheaper than replacing a bolt action rifle stock I had to cut down and they have outgrown. My sons have shot mine a fair amount so they are comfortable with them. They can upgrade parts as they go including building their own uppers in larger calibers if they want to rifle hunt slightly larger game like antelope. They also already know how to clean an AR!
I know a semi auto is not the best way to learn to hunt, and I know if they are not used properly they present a possible danger in the excitement of shooting a coyote, that's why I will do as suggested above and make them hunt with an AR single shot.
By the way, I have nothing against handy rifles, and I fully understand some people will think I'm crazy for buying my 10 year old an AR 15, but to me a gun is a gun is a gun and I see no difference, they are nothing more than a tool that I am teaching my sons and one day my daughter how to shoot, own, and take care of with all appropriate safety and respect.
Thanks for the great input!