I've lived in a big city for years now. Never seen anybody get mugged, or shot, or carjacked, despite doing activist work that often has me visiting poor minority neighborhoods.
The only time I ever really felt uneasy was when I had to walk alone at night through a neighborhood where all the businesses had bars on the windows. Worst thing that happened was a couple of people asking me for money, and they didn't give me any shit when I said I didn't carry cash.
But any time I visit the small town where I grew up there's always someone or another acting like I came back from a fucking warzone lmao
Lots of good comments in here, but another big factor is that people suck at dealing with large numbers. They'll hear there were 300 murders somewhere in some year and think that place is a shooting gallery because they don't know the population of the city, and if they did they aren't going to intuitively grasp how rare crimes actually are.
And of course media has been banging the drum on crime for the past ~40 years despite crime lowering significantly over that time frame.