Once you start justifying authority and 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 (or should be) 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. They say anarchy only opposes unjustified authority. They of course never explain who gets to determine which authority is justified... I assume that determination is made by a further authority? An authority that is also justified? And which authority justified that authority..? It's ridiculous for an anarchist to go down this justified authority rabbithole.
A carpenter might be good at making cabinets, an expert at it even, but that doesn't make them an authority. Their talent doesn't give them the right to assert authority; power over anyone.
Authority is not simply an isolated instance of a person using force. Authority is a distinct on-going social relationship between people. A coercive relationship that has been legitimized by our authoritarian hierarchical society. It's a relationship where authority figures assert power over less-powerful individuals in their care. These individuals are expected to submit to this mighty authority figure and obey their commands unwaveringly.
As an example, imagine you're walking home at night and someone jumps out of the shadows and tries to stab you. In the resulting scuffle, you kill them in self-defense. This was a simple use of force; it does not make you an authority over the person who tried to kill you. This isolated action you took to preserve your own life does not magically imbue you with the authority to go on a killing spree.
Similarly, when your child is about to walk in front of a speeding truck and you grab their hand to stop them, you're not using authority. You're using simple force. A temporary spur-of-the-moment action to preserve life is not authority. It doesn't give you ownership over the person you're helping. Anarchy has no qualms with the isolated use of force, just the institution of authority.
Noam Chomsky frequently uses the "saving a child from being hit by a car" example to explain his concept of "justified authority". As far as I can tell, the people that repeat the 'justified authority' fallacy are all parroting Chomsky's views. He says:
“Authority, unless justified, is inherently illegitimate and the burden of proof is on those in authority.”
He insists that a person's authority can be legitimized if justification is provided for it. But of course, he misses a step by neglecting to explain who gets the authority to judge that the authority figure's justification is legitimate...
His definition of authority is inherently flawed. If he'd just say "force" instead of authority, there wouldn't be so many confused Chomsky-acolytes out there making arbitrary justifications for all kinds of hierarchical shit and then branding that shit "anarchist" when it's anything but.
Chomsky is never a good source for what anarchy means. He's made a career of watering down anarchy to better appeal to a white middle-class North American audience. Far too many anarchists look to Chomsky as an authority.
He also equates anarchy to the enlightenment and classical liberalism in his talks and writings, 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. While it's true that the political movement that branded itself as anarchism originated in Europe, anarchy existed in every corner of the world, long before European philosophers began to pine for a return to it.
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 minarchists and liberals that call themselves anarchists and they keep repeating his flawed definitions to newcomers, creating further confusion that echoes for years.
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.