Once you start justifying hierarchy, you twist a knife in anarchy. Ever hear the phrase 'all power corrupts'? It's not a meme; it's the entire reason anarchy exists as a practice.
Legitimizing authority enables archy. Doesn't matter if you call yourself an anarchist while justifying hierarchies you personally approve of for whatever reason. NO authority is legitimate in the eyes of anarchy. Yes, even in a parent-child relationship.
When you legitimize an authority, you're granting it power, presenting it as an institution that needs to be obeyed at all costs, and it won't stop there. It'll want more power because that's the nature of power. Always grows, never stops to examine its devastating effect on its surroundings. Power is a license to do harm. Whether it was your original intention to enable a violent force of power when you legitimized an authority is irrelevant. It will do harm and the people who signed off on legitimizing it are culpable for that harm.
Anarchy is the opposition to authority. To pretend otherwise would be a blatant misrepresentation of what anarchy is.
A lot of people confuse expertise for authority and then use that confusion to insist anarchy doesn't oppose all authority.
A carpenter might be good at what they do, an expert even, but that doesn't make them 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.
Consider a simple example: a wild beast attacks me and I kill it in self-defense. This is an instance of the use of force, it is not an instance of authority. Consider another example: I notice that my friend is in the path of a speeding car and pull them away. Again, force - not authority. Anarchy takes no stance against force, just authority.
People that repeat the 'justified authority' fallacy are parroting Chomsky's views, as seen in this interview.
Chomsky is never a good source for what anarchy means. He's made a career of watering down anarchy to better appeal to liberals. This whole confusion seems to stem from his flawed definitions. Far too many anarchists look to Chomsky as an authority.
The term 'legitimate authority' he uses in this video is specifically what leads to so much confusion with Anglo Anarchists.
Instead of saying "anarchy is against authority and hierarchy", he makes the mistake of saying anarchy is only against 'illegitimate authority' which is baffling because all authority is unjust to an anarchist. Pulling his granddaughter out of the street isn't an example of authority, it's an example of force. Saving someone from being hit by a car has absolutely nothing to do with authority.
He also equates anarchy to the enlightenment and classical liberalism in this interview, which is a very western-centric thing to say, especially since the enlightenment oversaw the divvying up of Africa by European imperialists and other horrifically racist and genocidal acts.
I don't consider Chomsky to be an anarchist (because he's demonstrably not one) so his definitions aren't that important to me. But unfortunately they're important to a lot of people that call themselves anarchists and they keep repeating his flawed definitions to newcomers and create further confusion.
Saving someone from being hit by a car has nothing to do with authority. That's a fundamental misunderstanding of one of the most basic concepts of anarchy.
Every shitty political ideology out there claims to be for justified-authority and against unjustified-authority. We know it's horseshit when they deem bombing school buses 'justifiable' 'collateral damage', so why would we adopt their dangerous doubletalk to define anarchy? As soon as you start making allowances for authority, you've stopped supporting anarchy.
Changing the definition of 'authority' to make allowances for 'justified authority' as Chomsky is attempting is a pointless exercise that only confuses the uninformed and gives us baby-anarchists who come in not understanding the basic definition of anarchy.