Use of logic and emotion are both fair, I've never had to justify my beliefs in the right to self-defense, but I could do it in my sleep. It starts with "If I didn't care so much about you" and ends with "would you rather identify my body at the morgue, or pick me up at the PD after I give my statement?" Some other ammo to use:
You can't make an appointment for an emergency.
Bad guys are already armed. I just want to level the playing field.
I'm not a cowboy, I just like the idea of coming home to you every night.
Are you willing to hope the police protect you, when I'm right here, and they're not?
You also need to get her to the range, and see what it's all about. Most women feel "empowered" by learning to shoot, it brings out the she-wolf in them. But if you're not a patient teacher, take her to a pro, and let him show her how good a shot she can be, without the emotional problems that couples can get into.
BTW, after teaching several dozen women to shoot as a police instructor, I'll let you in on a little secret. Most women learn to shoot well much faster than men, because they don't have a lot of pre-conceived notions, nor all the macho stuff that gets in the way. They tend to listen better, absorb the subject matter better, and shoot better. One teeny little woman I coached was shooting two-inch groups at 15 yards after an hour, and then turned to me and asked, "Am I doing okay?"
I assured her she was, then after she left I shot up 150 rounds, trying to equal what she did the first day she ever shot a handgun!
Papajohn