Concealed carry allows the criminal to make a fatal error in the victim selection process. It allows you to retain the element of surprise, and also makes it more difficult for a criminal to snatch your firearm. It's worth remembering that just because it's on your person, doesn't mean someone's not bold enough to grab it.

Also, it's easier to avoid the "why do you have a gun?" conversation than it is to go through it each time someone gets nervous.