I think anarchism is more about removing hierarchies, including gender roles and man's domination of nature.

The issue is that a governing body is pretty much always formed after some time. Murray Bookchin was an anarchist for a while, before creating a new idea of communalism.

It's essentially the idea of hyper localization, and democratic self-governing of small communities. The communities then delegate an individual to discuss larger issues with neighboring communities.

Bookchin also analyzed previous anarchist rebellions to see how they failed and why. He identified one of the largest contributing factors was that once the previous government's politicians were overthrown, the anarchists refused to "take power" and preferred to do nothing.

While the anarchists did anarchy things, capitalists went right back into positions of power unchallenged. Which is why Bookchin was no longer in supportof anarchism and developed a new philosophy. Which is actually being tested right now in Rojava.