A big problem with anarchy is that it's really complicated and is usually either misunderstood by the proponent or the listeners. Anarchy is about levelling the playing field and reducing the power that the most powerful structures have in our society. The problem of removing power structures in institutions, is that they will naturally get replaced by other ones, and the replacements are often as authoritarian as the originals.

In the US, it's popular to think that you can somehow replace elected government (where power is somewhat dependant on votes, and somewhat dependent on advertising budgets/capital) with business (where power is dependent entirely on capital), and that somehow this is more "anarchist". This is a naive idea.