...Her concern is also not my reaction to a situation as I am very level headed and have a long fuse. She is more worried about other peoples reactions should they notice that I am carrying.
I dont know that this is a fight I want to take on.
Ask her why she is more concerned with the non-threatening possibilities than the threatening ones.
Does she really fear that some harm will come from another person's disdain or possible comments? That forgoing a very appropriate means of defending against an actual criminal threat is a wise solution?
Bring the emphasis of the discussion back to safety.
And, of course, carry regardless. Some duties trump marital consensus.