Well, my wife is anti-gun and anti-violence. She can't even watch violent scenes on TV. It stemmed from an incident that happened many moons ago in which a friend of her brother accidentally shot and killed his own brother with a handgun.
I explained to my wife when we moved that guns were widely available and that she had a choice. We could have no guns in the household and take whatever comes or have at least one and some means of defending ourselves or holding out until more help arises. A few weeks watching the news softened her up.
Even then, at first she only wanted me to have one. Then, whenever I cleaned them, she would go run errands. If we were going on a road trip, I had to 'sneak' the gun to the car before she got in and we departed. Serious paranoia.
So 5 guns later, she's much better. She's since gone to a gun store with me and looked over a range in use (via the safety partition). We practice regularly with my Beretta 96 and snap-caps so I'm sure she's comfortable with it if I'm away on a business trip.
I figure I just had to take some time to understand where she was coming from and try to address her concerns one by one. Took some time, she's not ready for her own pistol yet, but soon...