Fact: Guns prevent an estimated 2.5 million crimes a year or 6,849 every day. Most often, the gun is never fired and no blood (including the criminal’s) is shed.
Source: http://www.gunfacts.info/pdfs/gun-facts/7.1/Gun-Facts-7.1-screen.pdf, page 21.
There will be 2.5 million additional crimes every year if you disarm the law-abiding.
Why?
Because everyone knows that there is a good chance the person that just accidentally bumped into you is carrying. So rather then a extended period of chest thumping that devolves into violence the bumped says "Hey!" to the bumpee. Who, knowing that the person he bumped into is also probably carrying, says "Sorry!"
There is no, "What is this little guy doing" or "Big guys think they own the road". They know that when it comes to fire power they are pretty much equal.
There is nothing to be gained in status by taking it further. No one is going to think any less of the two because they let the incident drop. In fact by taking it further you have lost points on the social ladder.
And that is, in brief, why an armed society is a polite society.