Class isn’t authority. There are inter-class authorities, and intra-class authorities. In my opinion, the latter aren’t bad and are often cases necessary and useful, but that’s more into Marxism. Anarchism needs class analysis because it informs anarchists on what the weak points and points of contention in capitalist society are. The working classes stand in opposition not to any vague concept of authority, but instead are a part of a complex system of circulation, production, and distribtution that is regularly centralizing.

Anarchists that wish to decentralize society need to understand how to counteract this centralizing force. Marxists push it forward into collectivization and democratization, while anarchists instead typically go for prefiguration and community aid. In either case, though, these forces must be understood in order to act, and these forces are determined by class, as they aren’t simply abstractions but a real material system that functions in the material world.