It's important to Americans because it's been sold to us as a fictitious part of a national identity. The gun industry has very successfully crafted this narrative, to the point where so many people take it for granted now, but it wasn't always this way; this is a thing that developed in (depending on age) some of our lifetimes.

Here's a book that takes a closer look at how guns took on this sort of mythic role -- more special than other tools and appliances -- in American identity:

https://www.pamelahaag.com/books/gunning-of-america/