[@Meta] Well, seems I'm not checking the wordings correctly which leads to me having some questions and misunderstandings. Well let's leave that behind and argue on how anarchy could be better on the logical sense, as you described.

I'm convinced that if the governing systems would suddenly collapse, after the chaos had settled and communities had been formed, it wouldn't be any different from how it is now. There would still be a ruler at the head of the hierarchy who didn't go there because everyone thought he was a just and nice guy. He got to the top through exercising power and building influence, similar to how it is in today's government. He probably wouldn't give a crap about the people as long as he was in charge. In democracy they at least have to pretend, here he could just be a tyrant. So basically, he could become an oppressor and gather "votes" based on fear tactics. Wouldn't organizations with military training have the upper hand? They could easily force the general public to kneel before them. And the leaders would still fight among each other for different things.

It is given that there would be many other communities who valued freedom and the right for everyone to choose what they wanted and who they wanted for their leader if there was to be any. They could as well use a referendum to decide everything of importance. But I ask you this, knowing human nature, how many of those communities do you think would exist in compared to the ones with a tyrant as it's head?

And I'm only talking about communities and not isolated people because you would [b]need[/b] to be part of a larger community in order to raise your chances of survival. And that is the logical way isn't it? [b]Follow the way which raises your chances of survival?[/b] Isn't that what everything in this world thrives and lives for? To survive and leave a legacy?

[quote]In fact, the idea that animals can't operate on logic advances this argument because it shows that it is standalone, independent of thought (as is required of logic). You're conflating the idea of human desire and logic itself, which exists independent of humans. Logic operates on its own and isn't impacted by anything any of us think.[/quote]

While logic itself is independent of thoughts etc etc, it is a tool used by us to achieve what we want. The animals have come to behave that way as a consequence of years upon years of evolution as they learned how to best adapt with the environment around them. But how much is that really worth? We, humans, have exterminated hundreds upon hundreds of species. How far did their purely logical way of living get them when compared to us, humans who are facing overpopulation? Haven't we done better on the aspect of [b]survival and procreation[/b]?
As you said, on a purely logical level, anarchy like in the animal kingdom is naturalistically superior because the abstract values and terms that come with a governing system are removed, making everyone free. But isn't freedom another "abstract term"? Isn't the logical way  of every living organism to survive, procreate and assure the survival of it's legacy on this earth? How would anarchy be logically better than the system that we currently have if it lacks on that front? Or do you want to argue that humans would have a higher rate of survival in anarchy and as so the population would grow even more than it has today?