Not that I'm well versed, but the way I see it, the problem with anarchy is a lack of infrastructure. It's unsustainable on the large scale. You can have a town or a city be anarchist, but at the level of a state or country it starts to fall apart - at least in the modern day, with modern requirements such as internet, power grids, decently quick long-distance travel, and so on and so forth. 

You need co-operation on a huge scale in order to maintain these things, and that's extremely difficult in an anarchist society. Indeed, that's sort of why we ended up forming democracies in the first place. So unless you're going to massively technologically downgrade your life, anarchy is somewhat untenable.

(As I said, I'm not well-versed in this, so if anyone wants to correct me please do <3)