That sounds like a psychological condition known as hoplophobia. I think it's best treated by familiarising oneself with weapons of all sorts.
In general weapons aren't, in and of themselves, scary. It's the intent of the people carrying them which can be scary or not. Drunken half-wit shouting slurs? Scary. Single mother buying groceries with her kids? Not scary.
A sidearm on a belt is as inherently scary as a knife clipped to a pocket: not very, IMHO. It's all about the person carrying it.
As for why folks need weapons, IMHO arms-bearing is the fundamental difference between a slave and a freeman. I'd love to live in a modern Western society in which every adult carried a weapon of some sort as part of daily life, although I'm not wishful enough to think that our current society could do so safely.