I am wondering how an anarchist society would handle people who are trying to take control of the society. Anarchism is a system that does not involve any kind of coercion or oppression. It also seeks to abolish prisons. What would be done with people who want to control others? This is a natural part of human nature, as people want to have something for themselves and protect it, either alone or in groups. There would be people who oppose the new system. Is it possible to live in a world without any kind of oppression or authoritarianism? I believe this is a utopia.
What would one do with the supposed insurgents or people who want to govern the others?
1) Both Anarchism and Communism aim for the abolishment of classes, so that there will not be profit generated from human-to-human exploitation. In that sense, people of a classless society will not have the incentive to rule, as they will have nothing to gain from it. In the extreme case, that there are certain people/groups of people that won't leave their ruling positions, wish to remain in the ruling class or seek to have a ruling role for psychological reasons, they will be cast out from this society naturally.
2) Even in an anarchist society it still exists some form of "punishment", but certainly not suspending the freedom of the others, but more focusing on compulsory work for the society. Mainly, anarchists argue against prison system in the existing capitalistic system, which is used not only to protect the society against crimes, but as a political tool in the hands of the ruling class to express and maintain their dominance.
I think it's part of the animal nature of man to want something for himself and defend it
That's just opinion-based, not a scientific fact.
So is it possible to live in a world without any oppression or authoritarianism? I believe it's an utopia.
It is possible if the elements that cause oppression are removed. Historically, as an example, you can check the revolution of Slaves/Spartacus, the American revolution, the French revolution, etc.
A map of the world that does not include Utopia is not worth even glancing at.
There is FEJUVE or The Federation of Neighborhood Councils-El Alto that has been around since 1979 or 44 years. It has a population of over 114,000 people and according to the book Community Organizing and Rebellion: Neighborhood Councils in El Alto, Bolivia by Emily Achtenberg, has an anarcho-mutualist economy.
According to Dispersing Power: Social Movements as Anti-State Forces by Raúl Zibechi, FEJUVE deals with crimes and attacks on their free society by having volunteer mediators deal with minor disputes, and a collective self-defense group trained like a volunteer version of a police force to deal with dangerous criminals.
They wouldn't cohesively do anything because they would need to establish a formal hierarchy in order to act as a singular entity against a unified opponent. Anarchists don't believe in the establishment nor perpetuation of hierarchies and therefore they'd simply roll over one-by-one when confronted by an external threat. Not only this, the anarchist cannot ideologically understand such a thing as the existence of externality / internality would construct a formal hierarchy that is, itself, incompatible with the ideology.
TLDR: anarchism is incoherent.
In the Spainish Civil War there existed some of the largest groups ever calling themselves anarchist. They fought effectively against both political incursion of nominal allies and military incursion of enemies for a few years before being disarmed and destroyed.
I understand executions of traitors and spies was not uncommon.