I fully agree with you there mate

. In the past, European civilizations were probably responsible for some of the most systematically brutal, violent, warlike and expansionary behavior of any group of peoples ever to inhabit the earth (with the possible exception of the Mongols!

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But I think you mistook the point I was making. I wasn't referring to historical or nation-on-nation attitudes to violence, but rather to contemporary, domestic dynamics. I think it might help to look at the issue from a different perspective.
The end of WW2 led to very conscious post-war efforts to enhance the interdependence of European states. This was realized in practical terms through the development of cross-European institutions like courts and instruments of arbitration, through deeper and more complex economic links and trade arrangements, and now takes its form in the various institutions and treaties of the European Union. This peaceful cooperation (notwithstanding the exception of the former Soviet sphere, and now parts of Eastern Europe and the periphery...) marks a very definite break from those thousands of years of violence and competition. Frankly, Europe had no choice but to become more peaceful, since future wars like WW2 would probably have killed billions, European and otherwise, and left much of the planet an uninhabitable ruin.
This 'coming of age', and the incipient self-awareness among Europeans of the potentially catastrophic risks of intra-European violence (coupled to - and not by accident - the expanding capacity and responsibility of the state to provide cradle-to-grave welfare and security), also seems to be reflected in substantially lower levels of domestic violence (eg shootings, violent crimes, rapes, murders etc). And because of that, I think it safe to say the average European is generally now far less exposed to - and thus cognizant of - the risks of extreme or lethal violence in their day-to-day lives.
In consequence, and the reason for my waffly efforts at perspective above, I think Europeans often struggle to fathom why a people and culture that otherwise seems so similar and familiar to them (the US), would feel the need, or have reason, to normalize the ownership and carry of weapons for personal protection that can so casually and efficiently kill (often unintentionally) those around them? Naturally, this attitude and perception works both ways: many Americans are just as bemused by the seemingly illogical and laissez-faire attitude of most Europeans to their personal safety and security: what bizarre illogical people they are to have neither the willingness nor ability to protect their families, friends and livelihoods from violent criminals?
Clearly, the perceived risk equation in both places is radically different. And that's because the actual risks really are, objectively, radically different - to the point that violent crime, shootings and murder really are vanishingly rare events in much of Europe, even in some fairly large cities. More generally, I think cultural clashes over things like gun control illustrate the fact that when you're prepared to look deeper there are almost always logical (and often perfectly valid) reasons to support attitudes and preferences in one place that may, from the outside, look unfathomable, even alien, in another.
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FWIW I didn't bring any of this up as a point of judgement against the US, or to start a pissing contest with anyone. I have always understood to some extent the many valid and historical reasons for gun ownership in the US, and also why there are high(er) rates of violent crime. It just seemed relevant in the context it came up. And I think it's one of the more widely misunderstood ethnographical distinctions between us that, when analyzed, seems less irrational than the gut reaction might imply, and can help explain why rational cultures sharing such similar values can, nevertheless, arrive at contradictory outcomes and solutions.