No. Teaching and locking up are two different things entirely. Teach your kids by all means - hell, I learned how to handle and fire everything from a machine gun to a flintlock by the time I was 12 from a big time gun collector and long time family friend.
Locking up just means that when you are not around, the kid or someone else will not have access to it. If you specifically give the kid a gun, then that is on you. Kids are kids - they make a lot of mistakes. Showing and telling with a gun should not be something a kid should do - which seems to be the situation here.
I won’t address the locking up business. This has been widely discussed (and why most pro-gun supporters do not like/support trigger lock laws) and the consensus is that locked up guns are as useful as no guns for self-defense. As far as children are concerned, I would agree with your statement in the case of children that haven’t been trained on their use. This is sensitive ground, because I would not want to be the father of a child raped or murdered who may have had a fighting chance if they’d had access to the weapon. It’s a decision that needs to be weighed in light of the kid and his training. But I don’t think there is justification for a hard and fast rule.