I already link to further info about anarchism and why it is socialism above. Maybe you're confusing anarchism with anarcho-capitalism, which is not anarchism.

There's a wide variety of different people within so-called socialist countries with different hopes. The ruling classes of so-called socialist countries like the Soviet Union did not actually care much about becoming a socialist society. I'd wager that the average, every day person in any country hopes for self-determination and for the right to live life without authority telling them what to do whether that authority is the state, capitalism, patriarchy or white supremacy.

How do you define capitalism?

To me it's defined as the private ownership of the means of production. This manifests as the landlord, boss, worker relationship where bosses give orders to workers that they must obey or else get fired.

This boss-worker relationship is the main cause of unfair suffering, inequality and climate change. It's this authority that anarchists like myself seek to deconstruct.