There are a lot of statistics about guns and survival, and it's not 100% conclusive. Most "bad" firearms related deaths which happen to firearms owners are suicides, followed by children and stupid accidents, followed by domestic violence with guns. I'm unlikely to suffer from any of these.
Carrying a concealed weapon (where legal) has a lower benefit than carrying a cellphone and first aid/trauma kit (which I also carry, and will try to get to EMT-I certification again, if not paramedic), but I still think it's a net improvement in your personal safety, assuming you're trained and competent.
The biggest disadvantage is that in some states you can't go into a restaurant where alcohol is served (even if you're going for a meal and don't drink), and of course the fashion compromise of a 1-4 pound hunk of metal/plastic/wood.
I think most gun owners disbelieve "invincibility" even more than non-gun owners when it comes to guns -- handguns especially are fairly non-lethal (at 3', I'd rather have a knife), and give an advantage to he who initiates violence. I'd be very happy to trade a firearm for a Dune-style shield or something.
I think another factor is that a responsible gun owner who is carrying is probably more likely to avoid places where an incident might happen -- aside from bars, I'd also be a lot more likely to be less confrontational in traffic or other situations if I realized there was a potential it could escalate to shooting. I've never been involved in any kind of scuffle or anything while carrying a firearm, and while I actively avoid "bad areas" to the extent possible no matter what, it's another factor. Although I am willing to stop to render aid to stranded motorists when armed, whereas unless it's a very clearcut situation, just drive on (and optionally call 911) otherwise.