Actually we don't.
South Africa has many more guns in circulation than we do and their murder rate is many times ours.
Switzerland has gun laws similar to ours and their murder rate is miniscule.
Are those datapoints "outliers"? What is the overrall trend,, rather than the extremes?
Actually it's really hard to support a "cause and effect" relationship with gun ownership and rates of crime both pro and anti, because many factors go into crime rates and international laws and definitions of crimes (such as homicide) can vary.
South Africa has a great many factors at play that do not exist here including far more poverty and high high unemployment in many districts.
Switzerland is a very different society than ours - it's a tiny country, homogenous in culture, and has a culture that is very law abiding and socially responsible. Hard to make comparisons.
More realistic comparisons would be with countries that have more diverse populations and a similar culture to ours, such as Canada.
It is interesting though, to notice where the U.S.
lies in the rankings. The countries with worse rates are predominately Third World and/or politically unstable. Much of the "developed" world has much better crime rates, including countries with legal systems and definitions similar to ours and more restrictive gun laws.
Among the countries with the best rates are some of the Arab countries but then - they have the harshest punishments and don't necessarily recognize violence on women as a "crime"....
UK and other European countries have significant immigrant populations that contribute to crime rates yet still have a far lower incidence of violent crime.
But one point missed is this: if it is true that more guns lead to more crimes, why have rates declined over the last 2-3 years (plus) while gun sales have gone up? If the proposition is true then increased gun sales would end up with increased crimes as a result. And they haven't.
I don't necessarily support that contention - I think too many factors influence crime rates to say with any certainty that more guns or fewer guns make it or break it.
If crime rates have declined in this country - is it solely due to increased gun ownership or is it other factors such as stricter penalties?