You are still confusing two different questions: whether authority exists, and whether authority serves oppression or liberation.

Authority does not stop being authority because it is used for a good end. A shovel used to dig irrigation channels and a shovel used to murder someone are still both shovels. The moral and political content changes, but the object itself does not.

So when I say collective decision-making can be authoritarian toward the minority who disagree, I am not saying it is politically equivalent to a kingdom. Obviously a peasant commune, a workers’ council, or a revolutionary party has different class content from a monarchy. The difference is in form, class basis, and whose interests are being served. But if a collective decision is binding, and if the minority must obey it, then authority exists.

That is precisely Engels’ point. He is not claiming that all authority is identical, harmless, or above criticism. He is arguing that anti-authoritarians often pretend they have abolished authority when they have only renamed it.

The real distinction is not “authority versus no authority.” The real distinction is authority in whose hands, serving which class, under what material conditions, and for what purpose.

A kingdom concentrates authority in a dynastic ruling class. A revolutionary collective uses authority against exploiters, saboteurs, invaders, landlords, capitalists, and sometimes against backward or individualist tendencies among the people themselves. These are not the same political phenomenon, but both involve the social relation that is authority.

A village deciding collectively to redistribute land is exercising authority over landlords. Workers seizing and planning production are exercising authority over capital. A revolutionary army maintaining discipline is exercising authority over its own members. Public health measures, food distribution, irrigation, education, defense, and production all require binding decisions. Calling this “coordination” instead of authority does not change the relation.

Also the western anarchist idea of a “political class” or “administrative class” is a delusion that does away with the basis of what constitutes a class. A class is not simply “people who make administrative decisions.” A class is rooted in relation to the means of production: ownership or non-ownership, control over production, and the ability to privately appropriate surplus. A landlord, capitalist, slave-owner, or imperialist bourgeoisie is a class in that sense. A delegate, cadre, militia commander, village official, or administrator is not automatically a class just because they exercise authority.

Can administrators become separated from the masses? Yes. Can bureaucracy become a real danger? Yes. Can a socialist state degenerate and restore capitalism? Yes. But this does not mean administrators or politicians constitute a separate class unto themselves. It means that administrative and political positions can be captured by, subordinated to, or made to serve other class lines. The class character of these positions is determined by the social relations they reproduce: whose rule they enforce, whose interests they serve, and whether they help maintain or transform the existing relations of production. In a proletarian state, administrative authority is supposed to serve proletarian rule; under capitalism, it serves bourgeois rule. The position itself is not a class. “Political class” is just a vague moral category for “people with authority I dislike,” avoiding the real analysis of what class power they express, what function they perform, and what social relations they defend.

MLs do not make authority meaningless. We simply do not treat the word itself as something to fear or evade. Authority remains authority whether it is reactionary or liberatory; what changes is its class content, purpose, and historical function. It is a mistake is to pretend that authority disappears once it is exercised collectively, democratically, or in service of emancipation. It does not. It is still authority, but authority directed toward a different end and grounded in different social relations. MLs do not feel the need to constantly rename liberatory authority as “coordination,” “delegation,” or “justified force” in order to make it acceptable.

Marxists are more blunt: authority means the ability to impose a decision, compel action, enforce discipline, or subordinate one will to another in definite social relations. That can be oppressive or liberatory depending on class content and historical role.

A landlord’s authority over peasants is oppressive. Peasants’ authority over landlords during land reform is liberatory. A capitalist’s authority in the factory is exploitation. Workers’ authority over production is emancipation. Imperialist authority over oppressed nations is reactionary. Revolutionary authority against imperialism is necessary.

These things are central to what I consider authority.

That's fine if you want to define it differently according to your own standards, and think that if proletarians make laws and rules, being forced to obey them isn't authoritarian (although you would be going against most of your anarchist comrades with that definition, who consider any affront to personal liberty, "authoritarian").

Why? Are you some sort of anti-authoritarian?

Mao and every other ML are defining authority in the same way; all consider the dictatorship of the proletariat to be equivalent to working-class democracy, and democratic centralizsm. "Anti-authoritarians" staunchly oppose Mao and the DOTP, so you'd be in a tiny minority of anarchists if you actually support the CPC.