I'm in the UK and my partner, father and brothers have gun licenses. My son at around age 4 will be taken to the gun club to learn to shoot in a controlled environment. Why? Because it's quality time with his male role models It's just the same as when they'll take him fishing or archery to me. Maybe it's because I have grown up around guns that I don't find it so shocking, I'm pretty sure I shot a gun at a young age (it never interested me though). I think the difference is, that here in UK you can only really shoot real guns, not air rifles in controlled environments. We have guns in the house, in a cabinet which is securely locked, ammo kept in a separate cabinet and is vetted by the police every few years.
I'm sure they could bond in other ways, but when my son is 4 and seeing his Dad heading out on a Saturday morning with his Grandad and Uncles, it seems unfair not to let him when he is at an age where he can follow instructions. Plenty of children and families go to the gun club, I go occasionally, it's just target shooting
ETA: At no point in time will he have access to the guns outside of that controlled environment.
I think the main reason I don't like the thought of children handling guns with live ammunition is that a gun is aethsl weapon. And potentially it could kill them or someone else x
It's also a sport though. I see it as no different to karate or judo. He'll be taught to be respectful of guns and how to handle them correctly, I've never heard of anyone being injured by a gun at a gun club in the UK. I can't stop him being around guns due to his Dad loving them so much so I might as well let him be taught to handle them correctly and safely from a young age. I think that is why so many young kids are allowed them in US, because if they are part of your culture you can't hide them so it is safer to teach them how to use them correctly.