Anarchism with a class-struggle perspective” doesn’t mean it is “class reductionist” but that it disagrees with Bookchin and others who fail to see the continued reality and importance of the class structure that is at the heart of capitalism and the struggle that grows out of this. To change society, it’s not adequate to appeal to “humanity” or “citizens” in general, as Bookchin proposed. The capitalist and coordinator classes are also part of humanity but they are entrenched in maintaining their power and privilege. At the same time, the division of society along the various lines of oppression generates movements and struggles in opposition.
At its heart capitalism is a system of exploitation of people who are subordinated in the work process, and a continual resistance or tug of war ensues because of this… sometimes on a small scale, sometimes breaking out in large social events such as general strikes. Ultimately there is no liberatory replacement for capitalism unless workers are able to gain control over their own productive activities and potentials. If we take seriously the principle that “the emancipation of the working class is the work of the workers themselves,” it’s hard to see how this emancipatory result is going to happen without a movement actively developed by workers themselves.

— Anarchism, Class Struggle and Political Organization