I really have to disagree with you; a shotgun is much heavier than a handgun, which means it will be much harder to hold and aim than a small handgun. Granted, it also gives an almost guaranteed incapacitating shot, but what really matters in home defense is the fact that you have the gun and can kill the intruder if you so wish; that's enough to deter just about anybody. A shotgun is also much harder to load, so you either have to load it on the spot or keep a loaded gun around, and not everyone feels safe doing that.
And ten-year-olds may not stop a lot of crimes, but it would still be better to have them be able to protect themselves if the dire situation should arise. I imagine, for example, that the movie "Home Alone" would have been over within 30 minutes if that little kid had been able to brandish a loaded pistol.
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