Anarchy is not a gradual transformation of governance, it is a complete change of paradigm. Instead of organisation via authority and centralisation, organisation arises in the absence of authority. In order to understand how such changes can manifest it is worth looking into history to find a similar situations.

The most similar change in human history, which is relatively small compared to anarchy, is the fall of the monarchies and the rise of large scale democracy. Authority was not abandoned, but from a fully centralised system it achieves some greater level of decentralisation.

Nevertheless the move towards democracy was revolutionary. From our perspective today it seems trivial, of course democracy works and, given correct principles, it can create more prosperity and more security than any monarchy. But back at the time this was not clear at all. Nobody has ever seen democracy. It was a mythical idea that worked in an ancient greek city of philosophers thousands years ago and thats basically it.

The King IS Order

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Most people did not like the king and knew that monarchy has many serious flaws. But they still ended up supporting the king because they did believe that a society without top down authority would decent into chaos. Somebody has to guarantee safety and security and the necessary price for that is some level of corruption.

Thinking that the people will just decide to have laws and enforce them on their own was such a strange idea that few people did believe it could actually happen. Maybe in a small village where everyone knows each other, but in a country? Impossible. Surely democracy would bring chaos, bad decisions and foreign enemies would take advantage and invade.

When We Kill the King, He Will Just Be Replaced

The second thought that was common was the unavoidability of monarchy. When the King is dead, militias will fight for power and the winning faction will just establish the new Monarch. Not having an absolute ruler is an unstable system that cannot last. Someone will always end up on the top and create a system of power and authority.
The new king might be better or worse. So when your current king is not too bad better not revolt.

Anarchy

We see exactly the same arguments used against anarchy. Anarchy is a radical idea that exceeds the imagination of people. Nobody really knows how things would work out. It was never tested historically on large scales.

Therefore it is natural to repeat the old arguments used against democracy. There is no order without authority. Anarchy is chaos. Foreign powers will invade to take control. And anarchy cannot last. Rival factions will arise to reestablish authority. And if your current rulers do not suck too much it is not worth the risk.

But are these arguments actually correct? At least historically they did not do too well and humans are notoriously bad at understanding and predicting paradigm shifts.