There are a few problems with the position about allowing people to carry concealed firearms.
First, while it's true that some crazed insane gunman would probably kill less people because he would be stopped quicker, there are no statistics to say whether or not it would occur more often or not. Crimes of passion are just that. Someone loses their head and does something horrible. Since there's no way to screen out everyone who would lose it, it's logical to assume that if more of those who had the potential to lose it had weapons, there would be more gun related incidences. Whether or not the total number of people killed would rise or fall is anyone's guess. All the statistical analysis in the world is merely hypothetical.
Second, saying that if more people possessed guns it would deter criminals doesn't fly. Criminals know that jail time is a real possibility. If they aren't afraid of that, why would they be afraid of the possibility of someone with guns? Additionally, criminals, for the most part, probably do not think of the consequences while committing a crime (of course I leave out the conscientious person who is not the habitual criminal). It was many years ago (mid 80's I think) where PBS had a show on crime, where they interviewed cons and ex-cons. There was a mixture of murderers, robbers, and muggers. The majority didn't think about the consequences; they never even thought they'd get caught. Furthermore, when posed the question, they claimed that if they knew or suspected the victim of their crime had a weapon, they (well, the ones not in for murder) would have been more likely to kill their victim, rather than not commit the crime in the first place.
Finally, more armed citizens means more skittish police (is that person carying that weapon a rational, law abiding citizen or a crazed criminal?) I wouldn't want to be a police officer in such a situation.
HOWEVER...
On the opposite side, I also can't see how outlawing all gun ownership would work either. After all, as has been pointed out, criminals don't obey the law, so why would they obey the anti-gun laws? If a system could be put in place where there ere not just FBI criminal background checks, but also psychological analysis done to determine if the person is likely to go off the deep end, then I would be more supportive of concealed firearm permits.
The Supreme Court has regularly held that the Constitution is not absolute. For the good of society, they have ruled that some things are not protected, such as the "right of free speech" by yelling "fire" in a crowded theater. It seems logical to assume that for the good of society, they would see no problem regulating gun ownership, such as allowing laws that outlaw or restrict certain types of guns, carrying them in certain places, etc. Where the line is drawn is certainly a matter for debate, of course.