European civilization consists of a core, which is, by and large, Europe, and fringes, which are America and Russia(*). I guess life is rougher in the fringes. In Europe, gun violence or violence in general is rare enough that making everyone a well armed militiaman ready to use deadly force to defend themselves would be a complete overkill and pretty much only introduce the downside of every psycho being armed to the teeth. Few people can be expected bother to carry around military grade firearms or any firearms for that batter let alone be trained well enough to use them effectively and lawfully. That is not really even necessary.
*) Russians can buy weapons for hunting, self-defense, target practice and to collect them after taking mandatory gun safety classes and passing a test as well as a background check but Russians in general are not particularly crazy about guns despite the fact that Russia has a homicide rate that is twice that of the USA.
Yeah the comparisons between the US and Europe are always a stretch just because of the size and heterogeneity of the US. You can't compare the US to the UK because you also have to include Bosnia and other places that are poorer and where life is cheaper.
The vast majority of gun violence in the US is domestic (where it doesn't particularly matter if a gun is used or not) and gang violence. The random shootings like we hear about in the news are statistically rare in a population of 330 million people but get huge amounts of attention.
You're right. Because of the bosnias of Europe I added the modifier "by and large". And it's probably also true that some parts of the USA are much more violent than others.