Anarchism isn't no government, it's no state. The distinction between a government and a state varies between different definitions, but the most widely accepted distinguishing characteristic of a state is a monopoly on the legitimate use of violence.
For example, a high school club might have a system of government, with a president, treasurer, and secretary. But the club president has no greater right to the use of violence than any other member.
It may be hard to imagine a national government operating the same way, but I believe it is possible.
I hear you, but my foolish hope is that most people are either too decent or lazy to go around killing and stealing. I know every piece of post apocalyptic media swears otherwise...
It wouldn't be most people. If you had 100 people, 99% were good people but that one person has a gun and is willing to fight and steal from others, then all 99 are in danger.
And by post apocalyptic media, you mean the news? That's how people react. People are evil and we live in a fallen world.
