There is a huge gulf between can and should. Heck, my uncle was providing the family with food, by himself, with a 22 rifle when he was that age. He certainly was on his own while doing it, and he knew exactly what he was doing. BUT, that's not how kids grow up now, they don't have the same training, the same socialization.
Having armed 11 year olds at school is a recipe for heart-wrenching disaster. Rare individuals may do just fine with it, but for most, the lack of training and judgement will eventually show.
I've posted enough that I'll assume you are aware that a) I don't own a gun because I don't trust me b) I have a non-lethal weapon in multiple locations around my house c) I'm not "anti-gun.
That being reiterated, I want to ask what purpose guns have if you have to keep them locked up? Surely, in the middle of a home invasion, you're not going to run to the gun safe, enter 27 left 24 right 14 left flip the handle, open remove from rack, aim and fire. You're going to want the gun(s) highly accessible, loaded and ready to go. But once you arrange that, any body else can easily take them. A thief, a visitor, your grandkid Charlie etc.
So, how do you handle this? Inquiring minds etc.......
As you said his brain is still developing and will not reach its full growth until about age 18. Children mimic the attitudes and opinions of their parents. They want to be like them and so adopt these things which the parents are most passionate about. His future personality is being developed by his surrounding and those people in them.
IS this the way we want children to think or believe?
"Those who do not learn from history and condemned to relive it".
"There are those who will debate the necessity of wilderness, I will not, either you know it in your bones or you are very very old". Aldo Leopold - Sand County Almanac