the simplest definition one can give to anarchy is simply "anarchy is order". The basis of the state is to use a monopoly of force to separate people into different groups, so that one may control another. In capitalism it is capitalists and workers, in feudalism it is lords and serfs.
The basis of every system is using violence to suppress a specific group and/or idea. That is simply inescapable. The idea behind anarchism is to use that against the people who would wield it to divide the people into classes.
This creates a massive difference between anarchy and other systems. Other systems, to continue their own existence, must adhere to their own rules above all else. The best way to tell if a system is working, in the eyes of those in power, is if they continue being in power. The US revolution for example, all those years ago. The cishet white property owning man was the one in power before the revolution, during the revolution, and after the revolution. There was no real revolution, just a transformation of the power structure. The same group remained in power over the same group, they just decided to operate slightly differently. Do you think they would not have accepted Britains help if instead of their own revolution, the slaves had one?
To become ruling class in this society you must be willing to use exploitation to remain in the ruling class. If you are not willing to do that, you will eventually be reduced to the state of a worker and instead be exploited yourself. This means only those willing to defend their power structure will be in control of it. This does not just mean a defence from the threat of other individuals, or systematic changes, this also means threats nature brings up. The capitalists would rather refuse to end climate change than eliminate the system causing it. The priority of a ruling class can never be to humanity as a whole. We must end the existence of the ruling class if we are to survive as a species.