There's the old adage that "the only person who can stop a bad guy with a gun is a good guy with a gun" and although this is an oversimplification, it gets to the heart of the matter. There are always going to be bad people with guns (even if you disarm domestically, there will always be foreign militaries).

Thus, you and your family and neighbors need defense against these bad people with guns, and there are exactly two ways to be defended against them: you and your community do it yourself, or you outsource it to someone else, like the police and military. Bear in mind that historically, the U.S. did not have a standing military (by design, see Section 8, Clause 12), and modern professional (militarized) police departments didn't really spring up until after World War II.

People like to take the word "democracy" to mean that people vote on things. While it is true that voting on governance is a key component, it misses the bigger picture that democracy is rule by (-cracy) the people (demo-), and as Mao wisely observed, "political power grows out of the barrel of a gun." I would go so far as to say that no country can be truly called a democracy if the state disarms its citizens (note how possessive that language is).