Even for squirrels, I prefer a .410 with bird shot.
I think a big mistake parents make is to switch a kid from his bb gun to a .22 rifle.
He fails to realize the difference. There's no kick and practically no sound. He doesn't realize that he's shooting a high powered rifle that will kill just like .300 Magnum.
I disagree that a .22 is a good gun to learn on.
I got my boys a .243 and a .270 for their first rifles, and they knew they were shooting a rifle, not a bb gun.
Such was a rig my Dad mandated for me and my siblings. We proved our selves on such before we were able to go unsupervised. Lordy Help us if he caught us goofing with a gun after that. I think my butt still has size 12 boot scar's on it .....He'd kicked us so hard when we did something unsafe......child abuse by todays standards ...Pure educational back then !.
Stay Safe !