A gun is a huge responsibility and meant to be a lethal weapon. It's main purpose is to kill. To give children the tools and training to kill something is a cause of concern. Is it their responsibility to shoot intruders? Accidents happen and it is irresponsible to put a child in the position where they have to deal with the consequences of a gun accident. Guns are not entertainment akin to a visit to a theme park. Firing an Uzi isn't some right of passage that proves they are a grown up or a cheap thrill. Shooting for sport, hunting or self defence wouldn't usually require the use of an automatic weapon as has been mentioned it is a miltary weapon. People should not be allowed to shoot these weapons without military training this would prevent children getting into situations where they try to handle guns they are not equipped to deal with and parents from putting pressure on instructors to go against their better judgement.
It is not the owning of guns that I object to but the trivialising them that is the issue. Naming a range "Bullets and Burgars" does not inspire me with confidence. It emphasises fun and entertainment rather than safety or anything else. People who want to support the right to own a gun cite many reasons for the right to bear arms but not that they are super, awesome fun.
If you feel there is a serious reason to own a gun then perhaps it is time to review the way guns are treated and certainly people should be encouraged to treat them seriously and take responsibility for how they own, maintain and shoot their weapons and not be able to casually walk into a range and fire weapons as a one off fun day out. They need to be able to realise that movie and TV shows do not reflect the reality of firing a gun.