I would just add that people always need a leader, someone who will take a responsibility for their decisions. Besides, our brain is made up in such a way that we strive for organized structure.
People who support anarchism are just tired of the existing government.
People don't need a single leader. There were societies governed by elders and they functioned pretty well.
Anarchism wouldn't be able to sustain itself. At least that's how I see it. At some point people would start to organize themselves into groups because it would be easier for them to steal from others in a large group. At the same time others who would prefer a peaceful life would organize enclosed societies that would be able to defend better against those attacks. At some point the society would grow so much that it wouldn't be possible to rely information and coordinate everything without people who would dedicate their whole time to this task. That's how local governments would emerge.