I want to open up with saying that I deeply sympathize with the idea of anarchy. My current view is much like that of Thomas Paine's in Common Sense: "Government, even in its best state, is but a necessary evil; in its worst state, an intolerable one." So, I already agree that it would be ideal to have an anarchist society, as I see all government as evil. However, like Paine, I view it as necessary.
I do not see anarchy in today's world as viable for one primar reason:
I believe an anarchist society, if begun, would just be conquered quickly. There is historical evidence that this is what happens. The free territory of Ukraine, Revolutionary Catalonia, the Paris Commune: all of these attempts were quickly crushed by a powerful state. So, to persuade me, I need to know of a logical and solid plan to prevent something like that from happening again. I legitimately do want to support anarchy, but I am concerned it is just not probable whatsoever at the moment.
"Nobody realizes that some people expend tremendous energy merely to be normal."
-Albert Camus, Notebook IV