My answer to the specific question is, "Yes. Some should carry, and some should not." It is up to the individual to make the determination for himself; anything more restrictive will end up biting all gun owners in the arse someday.
One example of a person who should not carry a defensive firearm is my ex-wife. I tried and tried to get her into the mindset one should have if he or she is to go armed. She could not do it, she lacked the judgment to know when to go to the firearm, and she lacked the desire to go find out or train.
A good friend of mine also does not carry because his temper is too bad. He has never had any legal problems because of it, but in college and for a decade or so after, he could tend to get a little, well, martial about things. Instead, he has learned and taken to heart the issue of proper defensive mindset as much as any of us, with the only exception being that he does not carry a firearm. A guy like that, well, I'd say he's a mature and reasonable fellow.
Best,
Jon