It's not just teaching them about responsibility with a gun, it teaches them responsibility for all things in life.
A kid doesn't need to SHOT a gun to know that it's dangerous and you have be very careful and respectful if you handle it yourself, I'm sure every kid is told that, if they grow up with a gun in their hand or not. What do they teach kids at shooting range that you couldn't teach them at home? It's only HOW to shot a gun, but as kid you don't need to know that, as long as you couldn't fire a gun properly anyway. If you learn it at older age even under 18 years, whatever, as long as your hands aren't adapted to firing water pistols.
I doubt that a kid will approach traffic more carefully or will be able to shop alone if they are taught "this is how you shot the gun, you need it to defend yourself,oh, but also be very careful with it".
I doubt there will be any young kid (under 14 years old or so) that could really defend itself against an adult person (problem is as well that the gun isn't reachable quickly, if it is.... well good parenting, I'm sure there are more accidental deaths , than deaths that could have been prevented if the kid had a gun).
@Xant You can upbring a kid successfully without teaching them how to fire a gun. As it seems it works better in all other countries than in the USA.