It all goes down to "winning". In movies like the Die Hard collection, the guns aren't the big thing -- winning is, because Americans have a notion that we have to win... at all costs. It comes from a number of strands in history, but the worst is where it is married to the Puritan moral streak, a place where the 'Kingdom of God' is supposed to triumph, and the Kingdom gets associated with America, and the need to triumph gets personalized -- and the Puritan streak approves of violence to win.
(thus a very brief summary of what could a a thousand-word essay)
Stir it together, and it's no surprise that Americans excel in violence of all kinds with and sorts of means.