I stand behind you in line at the store with a handgun either on my hip or under my shirt, and you don't notice; yet you are safer for having me next to you. I won't shoot you. My gun can't pull it's own trigger. It is securely holstered with the trigger covered. It can't just "go off", and cannot be accessed by anyone else.
However, rest assured that if a lunatic walks into the store and pulls out a rifle, I will draw my pistol and protect myself and my family and therefore protect you and your family, as I have purposefully and frequently trained to do. I may get shot before I can pull the trigger...but, I won't die in a helpless blubbering heap on the floor begging for my life or your life. No, if I die it will be in a pile of spent shell casings. I won't be that victim. I choose not to be. And I will not willingly allow you to be, either.
As for you, I don't ask you to carry a gun. If you are not comfortable, familiar with, and willing to use it in an act of deadly force, then please don't. But I am, and I would like to keep that right. The only person who can stop a bad person with a gun is a good person with a gun.