I believe much of the traditional American perspective on owning firearms is directly related to the American experiment of giving large amounts of freedom to its inhabitants coupled with a relatively large geographic expanse. I will take these two ideas in turn.
First, when Benjamin Franklin stated that "Those who would give up essential Liberty, to purchase a little temporary Safety, deserve neither Liberty nor Safety," he not only encapsulated the ethos of the American experiment, but he did so in the context of European settlers in Pennsylvanian defending themselves from attacks from Early American tribes (this has become a popular quote in favour of American civil rights, but the context is often ignored - here is the original source:
https://founders.archives.gov/documents/Franklin/01-06-02-0107 ). No one can convincingly argue that more guns in the hands of totally depraved sinners is not safer than less guns. But one gun in the hand of one unredeemed sinner is enough to warrant others the liberty to have them.
Secondly, factoring in the vast expanse of American territory and this liberty largely becomes a necessity in order to keep the 6th Commandment (as many have posted above). The closest police station to my residence is more than 15 miles away. There is a reason gun ownership and opinions on the topic are largely split along rural/urban lines. Not only do I have a greater chance to encounter human predators without timely police protection, I (and my livestock) also have a greater chance to encounter coyotes, foxes, and bears than my urban/suburban friends.
Since the OP is from the UK, having lived in the UK for several years in the 1990s, I recognize there is a difference in how gun ownership is viewed amongst us. But I would argue that even in the UK there is still a distinct difference in the perspectives in rural versus urban areas (though less distinct than in the US) as well as by region (as there is reported to be in the US). For example, I noticed a different perspective on firearms when I was living in Scotland from when I was living in Northern Ireland. My Highland friends in Scotland had shotguns to hunt grouse. My acquaintance in a Nationalist area in NI could not acquire a shotgun while my family members in their Unionist neighborhood possessed handguns.
Lastly, we Reformed folk are usually originalists in reading the writings of our spiritual forefathers. I would suggest we in the US need to also do so when reading the 18th century founding documents of the US. For example, the word "regulated" in the phrase "well-regulated" of the Second Amendment does not have same meaning that it does today. If we are not careful reading this language, we risk violating the Ninth Commandment: "Q144: What are the duties required in the ninth commandment? A144: The duties required in the ninth commandment are, the preserving and promoting of truth between man and man... appearing and standing for the truth... speaking the truth, and only the truth, in matters of judgment and justice... studying and practicing of whatsoever things are true, honest, lovely, and of good report." "Q145: What are the sins forbidden in the ninth commandment? A145: The sins forbidden in the ninth commandment are, all prejudicing the truth... especially in public judicature... speaking the truth unseasonably... or perverting it to a wrong meaning, or in doubtful and equivocal expressions, to the prejudice of truth or justice... misconstructing intentions, words, and actions...."