I think it's widely accepted that anarchy would be a terrible thing for society, and indeed would probably obliterate society completely.  I think so, too.  I remember being in unruly classrooms when the teacher stepped out for a moment and I wouldn't describe them as great situations.

Still, there's part of me that wishes humans could exist peacefully under anarchy.  The idea of no authorities and no rulers appeals to me on some level.  After all, the laws we're required to follow were all formulated by fallible humans and the authorities we have to obey are also these same fallible humans.  It would be wonderful in a lot of ways to exist in absolute freedom and not be beholden to the rules of society.  

But humans aren't capable of doing that in any kind of peaceful or just way, I don't think.  Even in our supposedly lawful society crime exists and people bend the rules to benefit themselves.  Many of the chief perpetrators are our so-called authorities, who are once again, fallible humans.  But if they're willing to do such things even when laws and rules are in place, imagine what they would do without any.

The other thing I think just wouldn't work under anarchy is the sort of unpleasant but necessary tasks that are essential to society.  Who would haul away trash or maintain sewers?  

The system of appointing fallible humans as leaders is far from awesome, but unfortunately I fear anarchy would be even worse.  I wish people would just be cool, man.