I’m not afraid of guns, I’m afraid of putting guns into the hands of people who may use them to hurt me.
Police are less likely to use guns to harm innocents. There’s nothing magic about it: they have selection criteria (not every citizen can become a police officer), they undergo training, and all uses of their firearm are investigated. There is no inconsistency here.
My thought experiment is just that; you don’t have to wonder why people would want to have nuclear devices. Just imagine that they do. Would you feel safer? Or would you worry that one of those people would be crazy enough to use their device?
Because that’s _exactly_ the way I feel about everyone carrying a gun. I would worry that someone would be crazy enough to use theirs.