It rarely has to do with a genuine concern of intruders and more to do with gun culture. Most of the time, people just own guns because they like them. Gun collecting is a hobby, as is shooting for sport (hunting, field shooting, clay targeting, etc.)
It's a large part of American culture because of the 2nd Amendment. Conservatives in particular often feel a sense of American pride and responsibility to own firearms. But lately, with all the proposals around expanding gun control due to all the gun violence and mass shootings everywhere, it's only amplified the conservative sentiment.
To many, gun ownership is viewed as a central cornerstone of American culture and patriotism. Naturally, guns are a tricky topic for Americans on both sides of the issue.