How are you expecting society to run without a Government?
Im really hoping you dont say "The Corporations will look after us"...
Don't worry, anarchism holds several schools of thought, of which I consider myself a student of many, but anarcho-capitalism is not one of them. I prefer the current system of government over a corporatocracy (although, we are getting pretty close to the point where the distinction between the two will be unclear)
I would agree with you if all of humanity was perfect. But humanity isn't perfect. The moment it's perfect, we can be anarchist without society falling apart.
While, ideally I'd like for there to no government anywhere, I recognize how unfair that is to all the people who do. In my mind, today, anarchism could work in a similar way to many communes and places like Revolutionary Catalonia. In that, people who to live a society without any solid rule, could, they just need some countries to give up the acres and acres of unused territory to classify as for that purpose.
It'd be dangerous, uncivilized, and certainly an unpredictable experiment, sure. But we have enough successful examples of small anarchist areas being run peacefully and successfully that I think giving people the choice is paramount. The people don't need to be perfect, slab city, communes, and other places that run with little government intervention aren't perfect (see
Tower of David,
Kowloon Walled City) But they aren't in flames, in the Tower of David's case it absolutely worked when the government wasn't there, and in Kowloon's case it's improving with minimal government assistance, I think that's a step in the right direction.
All of humanity doesn't need to be perfect, we just need a group of people given the opportunity that are willing to try.