He treats Marx’s theory of alienation as Marx’s definition of capitalism.

He misreads “co-operative property of the workers themselves” as supporting predominantly workplace-level ownership.

The Engels “national capitalist” quotation is badly truncated conceptually. Engels absolutely does say that nationalization by the existing bourgeois state does not magically abolish capitalism. But the same passage proceeds to say that the proletariat seizes political power and initially transforms the means of production into state property.

The Chairman Mao quotation about “not eliminating capitalism” is removed from its stage-specific context. Chairman Mao was describing the New Democratic transition of an overwhelmingly agrarian, semi-feudal and semi-colonial society. In the same 1949 analysis he called for moving from an agricultural to an industrial country and from New Democracy toward socialism, with the state-owned sector as the socialist leading sector.

“If socialism needs capitalist mechanisms to develop productive forces, then capitalism must be superior to socialism” is a non sequitur. Transitional concessions reflect the inherited material structure of society, not the abstract superiority of capitalism.

He compares forms while disregarding class content.

Also several of his arguments are internally inconsistent

He says anarchists do not fetishize cooperatives, then repeatedly uses cooperative workplace control as his principal empirical test of socialism.

He says anarchism is not opposed to transition, but defines the Marxist transition as capitalist because it still contains transitional categories.

He accepts economic and political compromises in Spain but treats comparable compromises in Russia or China as proof of counterrevolution.

He excuses anarchist projects for being defeated externally while using external defeat against ML projects.

He says local institutions must federate into an integrated economy but treats centralized integrated economic decision-making as worker alienation.

He says capitalism can only be overcome through long historical transformation, yet faults the Bolsheviks for not abolishing money, commodity relations and inherited bourgeois norms almost immediately.

He correctly insists that socialism cannot merely mean better welfare, but then fails to seriously analyze the abolition of private capitalist ownership and planned social investment because his definition already excludes state-socialist ownership.

He rejects state ownership because ownership must belong to society itself, but never adequately solves how “society itself” makes binding macroeconomic decisions except through federated institutions, which are themselves organized political power under another name.

There are too many to be worth time fully recounting but his entire premise is using Marx's descriptions of some qualities of capitalism as making a society either simply capitalist or not. This is the exact antithesis of what Marx is doing in defining or highlighting those terms and phenomena and not at all in line with what he was doing, e.g. saying, "you're only abolishing capitalism if all these things are gone!" It just makes no sense at all if you have actually read Capital, and I am confident Anark is either lying about having done so or is intentionally misleading.

Let's take alienation from the commodities one produces. Would you like to tell me where Marx says, "under socialism this will just be gone"? Marx is actually describing his conception of the development of capitalism from precursor relations and how its dominance appears, hidden in society. There is absolutely nothing in it that says, "every aspect of capitalist society will go away once we have a real socialist revolution". That is actually the exact opposite of what Marx predicts, which is that the working class will simply take the society they have and begin it's transformation in their interests, oppressing the bourgeoisie in the process. And the full culmination of the working class being the final oppressing class will be communism, achieved via an extended struggle within a worker-run society. He describes capitalism as developing over hundreds of years to do similar things, albeit while maintaining class conflict with an exploiter class above (unlike the dictatorship of the proletariat concept).

I don't even remember exactly what Anark says about alienation from the product of one's labor but it's such a commonly misunderstood idea that I would bet that is also deeply flawed. Just mentioning this because it's my specific example, but the point I am making is about the larger idea exemplified in it.