People claim that that you cannot have an anarchist organization, as “anarchist organization” is an oxymoron, and anarchism by definition rejects any form of organization.

That’s not true — anarchism rejects authority. And you can have organizations without authority. You don’t have to have someone be the boss to have an organization.

An organization can be just a bunch of people who decide to do something together.

People set the agenda

A given non-authoritarian organizations exist because a given number of people decided to participate. And it is these people, who determine the agenda of the organization.

Hierarchy constantly changes

It is subtle, but you can also have non-authoritarian hierarchies as well — whenever there is some task at hand, the person most qualified to do it becomes the boss and the rest of the people follow them. Hierarchy changes constantly based on the project at hand e.g. when we are doing activity A, the person who is best at A is “the boss”, when we are doing “B” the same person might be at the bottom of the pyramid.

The cult of personality

In authoritarian organizations, the same people are in charge all the time. In order to make sense of that, to explain why is it the case to ourselves and to others, we portray these people as the ones who are best at everything. This is just a cult of personality. The belief that there are such people, that people are divided to leaders and non-leaders (a-la Ayn Rand) is probably the reason why authoritarian organizations exist in the first place. Dismantle this belief, this concept, and all that I said would make sense immediately.