Anarchists obviously don’t think this will come about by itself, they simply believe that it is possible to organize society in such a way that the statement above holds true. Anarchists will generally argue that todays society prevents that from being the case (at least to a large enough degree).
The details of all this (strategies, how to make it work, etc) is at the core of a lot of anarchist theory.
That's what I find so weird about most criticisms of Anarchism. Anarchists like nothing more than building systems and methods, then seeing how they work or could be improved. The only way to differentiate different forms of anarchism is through the systems they think would be most effective, and the methods they think would be most effective to bring them about.
It's just a lot harder to build peer-to-peer systems than centralized ones, although peer-to-peer systems are ultimately the most resilient.
Yeah, it's really funny how anarchism has this reputation for disorganisation. The anarchists I've met are super nerds about what is good democratic process going down to intricate details of how it all should be organised.
I guess there is probably also a big difference here between actual anarchists and people who merely sympathise with anarchism (like myself), possibly mainly because they have an anti-authoritarian inclination (which alone, an anarchist does not make).
The details of all this (strategies, how to make it work, etc) is at the core of a lot of anarchist theory.