My inclination is to say everyone should carry, after all the old adage "an armed society, is a polite society." rings true in my ears.
I live in a state that has recently passed "constitutional carry", in other words if you can own it you can carry it however you choose.
Now being able to do something doesn't mean that you should do something. We can all think of situations in which exercising our right to do something while completely legal probably isn't a great idea. First thing that pops to mind for me is going clothes shopping with the kiddo's while running full kit and carrying an AR-15. Totally legal, but not a good idea.
Natural law says everyone has the right to life and liberty. Guns go a long way towards protecting those rights. Everyone must accept they have a personal responsibility for protecting those rights. Unless you have the cash and inclination to hire armed guards, odds are high if you're ever the victim (or intended victim) of a violent crime you will be the one in a position to act.
So back to the initial question, should everyone carry a gun? I say no.
If you are unable or unwilling to;
1. Obtain some solid training
2. Commit to using deadly force
you shouldn't carry a gun.