You'd think the emotional argument on our side would be both easy and compelling:
Your daughter is about to be killed on the street by a madman with a knife. Would you prefer at that point that she have a cellphone, or a gun? Understand that if intervention doesn't happen within the next 5 seconds, she is dead.
If the choice is the gun, then you must support the right to carry a loaded firearm in public, because the gun won't magically appear in her hands -- she has to have it on her, and the time constraints are such that it has to be loaded and ready to use.
The cellphone is just a way she can inform someone else that she'll be dead by the time they get to her.