She's in Criminal Justice and she's irrationally terrified of guns?
I don't mean to pry, and please, do not feel pressured to reveal personal information on either your lady's behalf or your own, but it sounds to me like maybe she once had a pretty bad experience with guns? Tough spot to be in.
I sell guns, and one time at work some guy's wife was saying stuff like "This is ridiculous, why would someone need these awful things, home defense stuff is a bunch of garbage." A twenty-something female a few feet away handling a small-framed Glock said "Unless you get raped." Obviously, no one was going to ask her, but the look on her face did suggest to me that it was not a hypothetical, but she'd actually been raped.
Do you know anyone who's life/health was saved by a firearm? Or someone whose continued good health could have been? In my experience, meeting someone who was unarmed at the wrong time or armed at the right time can help convince an anti-gunner that a firearm has genuine value in the right hands.
Also, I think when I'm a father I'll be far more concerned about kitchen knives, swimming pools, car accidents, garbage disposals and cleaning chemicals than an empty, hidden, locked up gun.
Like someone else said, don't take relationship advice from Anonymous. I'd hate to see you break up with someone because of a message on a forum. BUT if I were in your shoes, I'd be less upset that my girlfriend disliked guns, and very upset that my girlfriend (apparently) refused to believe I was responsible enough to own something dangerous.