We see everyday anti-ancap anarchists (hereafter just "ancom") come here and share us videos/articles how anarcho-capitalism, or more accurately private property, is evil. Their main argument is this:

When there's a private property, there's also a power structure. In capitalist societies there's hierarchy, hierarchy means upper ranks have power over lower ranks which ultimately destroys individual's autonomy. Liberty notion of libertarians is deceiving and wrong because choosing your own boss is not liberty, it's like a slave's choosing your his own master. Also capitalism depends on state, state protects capitalist class against worker class. Without the state capitalism would cease to exist.

Ancom's these objections, however, are either empirically and initially wrong or true but also applies to any society (including their own vision)

Let's examine every point:

•When there's a private property, there's also a power structure.

True. But it's not about private property, it's about human interaction. Even if you don't have private property in the means of productions, you'll have power structure. Imagine there's a factory which run by a co-op of workers, like Worker's Council. Since these workers have the privilege to decide what to produce, they also have power on other people who don't work in this factory. The power structure is not abolished in this case, just transformed into a new one. Or in case of direct democracy, majority has power over minority, which is tyranny of majority. I wonder what is ancom's ideal society which is not based on power.

•In capitalist societies there's hierarchy, hierarchy means upper ranks have power over lower ranks which ultimately destroys individual's autonomy.

This is also true for every society. Ancom's may think that their society would not be based on hierarchy, but I wonder how will they avoid the iron law of oligarchy. There will be smart people, sociable people, hard working people, lazy one's, dum one's etc. Only way to prevent inequality and hierarchy would be using force over these people in which case we'll have also hierarchy, force and power structure. Wait, what was ancom's objection again capitalism again?

•Liberty notion of libertarians is deceiving and wrong because choosing your own boss is not liberty, it's like a slave's choosing your his own master.

I don't think ancoms understand liberty. Freedom includes the ability to choose your boss. How can mutually agreed contracts violate my autonomy? In capitalist societies you can work for somebody or be your own boss. Neither of these situations violate my freedom. I guess what ancoms think is that in capitalism we don't have many choices whereas in their utopia options are unlimited. This is missing reality; of course I'd like to be 6 ft tall, have 8 inch dick, to have time machine, to be immortal. But there are natural and social constraints. These are not imposed upon me by capitalism, these are the result of living in Earth and society. Capitalism doesn't narrow your options, on the contrary it widens them.

•Also capitalism depends on state, state protects capitalist class against worker class. Without the state capitalism would cease to exist.

This is straight outta Marxist class notion. However, there are no monolithic class structures. There's no single entity called "the Capitalist" or "The Bourgeois" or "the Proleterait" but there are millions of individuals whose interests are in conflict. It's true that governments grant favors to its cronies, but it's at the expense of other competitive capitalists State protects some of the capitalists/bourgeois against other capitalists and this is also true for working class. Think of tariffs: Tariffs favors domestic workers and capitalists at the expense of foreign workers and capitalists. Unions wants tariffs, minimum wages etc. so they can enjoy higher salaries. While domestic union member workers enjoy this, foreign workers are now in worse condition.

Classes are not monolithic. Also they are not cast classes either, there's mobility. It's stupid to think that the state protects capitalists as if there is a specific group called the Capitalist.

Ancoms are incoherent at best or directly intellectually dishonest. Probably both.

To quote Roger Scruton in his excellent work Fools, Frauds and Firebrands:

The old socialist complaint creeps in behind the Newspeak: where there is private property there is also power – the power of the one who owns over the one who needs, of group over group, of class over class. Always in the wake of the attack on ‘capitalism’ comes the yearning for a ‘powerless’ world. But this yearning, which finds its most eloquent expression in the writings of Foucault, is incoherent. The condition of society is essentially one of domination, in which people are bound to each other by their attachments, and distinguished by rivalries and competition. There is no society that transcends those human realities, nor should we wish for one, since it is from those things that our worldly satisfactions are composed. But where there is attachment there is power; and where there is rivalry there is the need for government. As Kenneth Minogue once put it: ‘the worm of domination lies at the heart of what it is to be human, and the conclusion faces us that the attempt to overthrow domination, as that idea is metaphysically understood in ideology, is the attempt to destroy humanity’. Our concern as political beings should be, not to abolish the powers that bind society together, but to mitigate their exercise. We should not aim for a world without power, but for a world where power is consented to, and where conflicts are resolved according to a shared conception of justice.