All kids are different
Recently at my ranges open day, we had heaps of kids want to try shootin' various guns. I was in the CAS section, so we had the Ruger single 6 22's and 22 leverguns. Some kids were 'with it' enough and could grip the single 6 firmly.... a few of them had a shot or 5 with a 44 mag Vaquaro.... some of these kids were quite small
but were well supervised (as in 'stood over')
Other kids, even bigger, 'boofier' kids werent holding the 22 firm or controlled enough (like holding a dead fish) and of course, for these kids the 22 was all they shot.
So, you have to look at each individual kid and arm them & teach them accordingly. You cant generalise and say when a kid is 5 he/she can ONLY handle a 22 (or airsoft) and when they are 7 they can instantly handle a 357 for example. You can usually tell what a kid can handle by their hold (firm & controlling muzzle flip), their understanding.... and of course their 'general ability'
Like adults, some 'have it' & some 'don't'...... some will 'learn & improve' & some wont! no matter what you do.
The most important thing is to know the kids temperament (if they get angry, will they do something stoopid?) they have to understand they have a deadly instrument in their hand..... If you think about it, you will know what stage a kid is at..... just be careful and have your 'eagle eyes' turned on at all times