do you think there is anyone who should not be allowed to own a gun?
It's a tough question, but the short answer is "yes, of course there are people who shouldn't be allowed to own a gun". And there already are those people. Convicted felons for 1. Domestic Violence offenders, I believe, for another.
But the long answer would probably be akin to, and I hesitate to use the anology, those people that aren't allowed to drive cars.