Hello again Dafing -
"...the country with the most guns, and one of the most violent..."
Mexico is far more violent than we are, and they don't allow any kind of guns for civilians.
"If these people realise others have a pistol, I would logically assume they would make sure they have an equal or if possible "better" weapon."
But you are making a fundamental assumption that all thiefs wish to become murderers. There is a large difference between someone who wants to steal and someone who is willing to kill to succeed at being a thief. But not everyone here has a gun - so a thief can still pick a victim who is unlikely to be armed. Studies have been conducted by the FBI (our national police) where career criminals say that their biggest fear is being shot during the course of their escapades.
"Think about it, if you are in a public place, say a movie theatre, watching, oh, lets say Avatar (in 3D if it makes a difference), would you rather EVERYONE had a gun, or that NOBODY had a gun?"
That point is actually moot, because in most locales, you are not allowed to carry into movie theaters even if you have a license. But it's also not a valid test because there are lots of people who frequent movie theaters who are under the influence of narcotics and other drugs - and those people are not allowed to carry weapons, and for good reason. But given a crowd who was licensed and had the proper training, yes, it is preferable that everyone is armed rather than nobody being armed.
"I would also think that if you want to commit a crime, and you know that the police who oppose you are brutal, you would be more likely to do ANYTHING you can to stay free. And thus things could escalate rapidly."
That is an interesting thought experiment but that's not the way it happens for the most part. Again, you're grossly over-estimating the number of psychopaths who are willing to kill. They are out there but few and far between.
"If you think that you live in an unsafe area because of weapons, then why add more weapons into the equation? Its a sort of a Mutual Assured Destruction theory? At some time, you have to back down, and work on REDUCING the problem itself."
Why add more weapons into the equation? I'll flip it around and say, if I know that the bad guys have guns, why would I make myself a willing victim by refusing to be armed? "At some point work on REDUCING the problem..." That is not practical. It seems that every time a country that already has firearms tries to restrict them, violent crime goes up. Why? Because the criminals, who don't obey laws anyway, will keep their guns while the law abiding citizens turn their guns in. Look at Britain for an example of this. Also, Chicago and other high-crime areas of the U.S. have the strictest gun laws in the country. This is not coincidence.
You should also consider why Sweeden was not invaded during WWII. There were a number of reasons for this, political, economic (they supplied the Nazi's wth iron), but each and every Sweede had a government-provided rifle and knew how to use it. Trying to invade Sweeden would be a nightmare under these conditions.