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Anarchism is just fundamentally anti-Marxist by the very nature of being idealist instead of materialist. There are endless words written about Anarchism, you can get incredibly deep with it, but the very foundation of it is individualist idealism so it's like getting deep into the fantasy genre or sci fi. It is a story centered around thoughts and emotions instead of a scientific process of social change centered around an analysis of material conditions, history, and economics. This is why it is has been so popular in the west, because you can just feel and think whatever you want and immediately feel better about yourself for being politically progressive compared to the people around you.

This is the ML position on anarchism:

The point is that Marxism and anarchism are built up on entirely different principles, in spite of the fact that both come into the arena of the struggle under the flag of socialism. The cornerstone of anarchism is the individual, whose emancipation, according to its tenets, is the principal condition for the emancipation of the masses, the collective body. According to the tenets of anarchism, the emancipation of the masses is impossible until the individual is emancipated. Accordingly, its slogan is: "Everything for the individual." The cornerstone of Marxism, however, is the masses, whose emancipation, according to its tenets, is the principal condition for the emancipation of the individual. That is to say, according to the tenets of Marxism, the emancipation of the individual is impossible until the masses are emancipated. Accordingly, its slogan is: "Everything for the masses."

Clearly, we have here two principles, one negating the other, and not merely disagreements on tactics.

— Anarchism Or Socialism?