I think there's cultural differences at play here too
For those of us from the rest of the Western countries the thought of having to strap a gun to yourself to go outside is very bizarre
Fear is the first thing that comes to mind
Look at it this way, when we think of the death penalty in countries like Iran, China, you think its because of their governments. That if the people had a choice they would vote no to capital punishment
Yet, even with the US's total mistrust of their gov, the people would actually vote to give the state the power to kill them.
I think the bolded is a key difference in perception. I don't "have to" strap a gun on when I go out the door, I "want to". I've gone most of my life without carrying and felt perfectly fine outside of 3 or 4 close calls. But having a gun in those 3 or 4 wouldn't have changed how I handled them.
The only cultural difference I can infer from the perception is that citizens of other western nations value their self-determination less. Personally, I want the freedom and responsibility to defend myself with lethal force should the need arise. I don't expect the need to arise or seek it, but I take pride in being proficient at that level of self-sufficiency. I also take confidence from the knowledge that in the unlikely even of a violent encounter, I have capabilities and options the aggressor may not.
I guess the primary difference, at least as far as I and some people I know are concerned, can be summed up as "we want the responsibility". Not many people say that, apparently even less so outside the US.
As for the death penalty thing, lack of faith in our legislators != lack of faith in our judicial system. I think our court system is about as good as one could realistically hope for in most cases.