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.