Not anyone and everyone is allowed to have guns in the US. Certain types of guns are also not for sale or are sold with restrictions. Hunting weapons can be purchased fairly easily, but most guns (here in California anyways) require a gun safety test, a background check (prevents sales to felons, the mentally unstable, anyone with a restraining order, and those convicted of violent misdemeanors), and a waiting period of several days. Fully automatic weapons have been banned since the 1920s, and anything of the "assault weapon" variety is also banned by federal law. Certain types of ammo are also banned or have been taxed out of existence. Here in California it's also illegal for felons to own or wear bullet-proof vests. Concealed carry of firearms is always illegal without a permit, and availability of those varies from place to place. Also, I don't think that kids under 18 are allowed to buy guns of any sort.
Not that I think that any of that is a bad idea, but almost all crimes committed with firearms are done so with weapons that were not acquired legally.
Frankly, the laws in Italy (when I lived their a few years ago) were much less restrictive than they are in the US.
What it boils down to though, is an historical tradition of the "right to keep and bear arms", which was placed in our constitution specifically because of abuses by the British Imperial government and the fact the rebellion against British authority would have failed had the populace not had private ownership of firearms. It comes down to the idea that the founders of the government wanted the citizenry to be able challenge the government if need be. A government with a monopoly on violence is pretty hard to get rid of. Kind of a moot point now as the firepower of US government far outstrips what a private citizen or group of citizens could ever acquire.