At the tender age of 6, you are asking a lot if you expect him to handle any more recoil than a 22mag. Even a 410 shotgun is too much for most 6 year olds, which is why most states won't let a kid start hunting until much later so game doesn't get unnecessarily wounded. If he missed 3 deer, maybe that is telling you something. As you have him practice, make sure and use the lightest loads/bullets available as even in a .243, all loads are not created equal. My son killed a 275lb mule deer at 325 yards at the age of 12 using a .243 with 95 grain partitions, and it performed perfectly. So if you are hunting 160 lb whitetails I am sure that a .243 shooting anything that will hold together on impact up to 200 yards will be fine. If you care at all about the game you are shooting at, make sure the gun fits your boy, he has had a ton of practice, and that if he doesn't seem completely comfortable when he is on the gun, don't let him pull that trigger. He will be bigger soon enough and if you instill bad habits(flinching) then it will be much harder to fix than you realize, as I've been there with my oldest son.
