I was never taught that violence was wrong as a means to solve problems - I was taught that irresponsible violence was wrong, violence out of all proportion to the situation at hand.
Screwed up interpretation of the Second Amendment of the US constitution has fostered a society very much entangled with the firearm. To an American, a criminal who ISN'T armed with a firearm is either stupid or unprepared. That's because IN America you'd have to be a moron to enter someone's house without a gun - chances are they're packing.
In the UK you'd have to be a moron to carry a firearm around, because the problems of doing so outweigh the fact that you could carry just about any confrontation provided you used your firearm effectively.
Police in this country have a habit of shooting armed felons VERY, VERY dead. They do this because we don't have an armed populace, and therefore public opinion says that someone only needs a firearm for nefarious uses, and that anyone carrying one deserves exactly what they get. Those that are captured without the firearm that the police have proof they used in a crime often face more jail time because of the existence of that firearm than they did for the offence they used the firearm to expedite.
So, to American's who don't understand how we can be free without guns, the simple answer is that we remain so, for as long as no other political group has them. You have guns as an equaliser - to us they are an imbalancing force outside of the norm.
This, of course, means that we don't SEE any good side to owning one. In our society there just isn't a reason for any law abiding person to do so. In your society, of course, it's like hanging a little sign marked "Rob me - I'm feeble" around your neck not to have one. And because of the risks inherent in burglary in the US only the most dangerous criminals do so - and they are more hyped up and tooled up than they'd otherwise need to be. This leads to an enhanced chance of violent confrontation.
Here are the figures, and these are all per capita, which means they've been adjusted for the difference in population sizes between the US and UK.
The US burglary and theft rate is 50% of that in the UK.
The US homicide rate is 570% of that in the UK.
The US rape rate is 300% of that in the UK.
So burglar's are deterred, but at a cost that you can judge for yourself.
What to do, though? It's not like strict gun controls will get the guns off the criminals, or remove the impetus for such crime. I honestly don't have a solution, but feel honour bound to point out that I don't think "more guns" is it.