I went and pulled up the numbers on gun-related deaths and gun ownership. I noticed that a majority of the gun-related deaths in the US and other countries like Canada and Switzerland were suicides. Presumably, some of the countries' gun-related death rates must be significantly unreported (i.e. Austria) because the numbers for some countries don't seem to include suicides.
In any event, I then decided to take a look at the suicide rates across various nations. I also looked up the murder rates across various nations.
Here are some observations and conclusions I reached. Feel free to point out any errors or omissions.
-People generally seem to prefer to kill themselves with guns when they're available.
-People also seem to generally prefer to kill other people with guns when they're available.
-Gun ownership rates don't seem to correlate much if any with overall suicide rates. Consider, for instance, suicide and gun ownership rates in Japan and Cyprus. The US does not have a high suicide rate and is below several European countries in suicides. Japan has an enormously high suicide rate.
-Gun ownership rates don't seem to correlate all that much with homicide rates. We Americans seem to like to kill one another more relative to folks in other western states, but are the exception rather than the rule. The Swiss seem disinclined to kill one-another despite their high gun ownership rates relative to other western nations such as France, Britain, and Belgium. For instance, Tunisia, which has the lowest or about the lowest gun ownership rate has a higher murder rate than Switzerland which has very high gun ownership rates.
-Gun ownership, as a practical matter, is not an overriding factor in suicide, murder, or intentional death rates. It probably matters a bit, but I suspect there are far more significant factors.
Here are some countries and their homicide, suicide, and total intentional death rates
High Gun Ownership Countries
US 4.2+12 = 16.2
Switzerland 0.7+11.1 = 11.8
Canada 1.6+11.3 = 12.9
Low Gun Ownership Countries
Japan 0.3+23.8 = 24.1
Belgium 1.7+17.6 = 19.3
Aside from the US, which is demographically anomalous among western nations in more ways than one, there really isn't a lot to say that gun ownership increases overall murder or suicide rates.