Archy: The Opposite of Anarchy
The dictionary definition of 'archy' is any body of authoritative officials organized in nested ranks. Be it a Monarchy, an oligarchy, a republic, a feudal state or any other hierarchical society.
While anarchy is the opposition to hierarchy, archy is the full embodiment of hierarchy. While anarchy calls for the absence of rulers, archy depends on the majority of a population serving and obeying a minority of rulers. Sometimes a few rulers (e.g. monarchies), and sometimes many (e.g. social democracies).
Hierarchies exist for rulers to maintain their social control & power over the population. This control is maintained with violent force by authorities appointed by the rulers: the army, national guard, police, courts, prisons, social workers, media, tax collectors, etc.
Not all guidance given by one person to another constitutes hierarchy. Choosing to accept a specialist's expertise in their craft needn't create a hierarchy or make them your ruler. A roofer laying your roof or a chef cooking your meal needn't be your superior simply because they are providing you with a valued service.
Similarly, an individual using force to strike a blow at the hierarchy that oppresses them does not turn the individual into an authority.
Authority is not simply an isolated instance of the use of force, but an ongoing social relationship between two parties. It is a relationship where one party has the socially legitimized right to command, and the other party has the corresponding obligation to obey.
Destroying archy where you see it does not create archy, it creates anarchy.