You are mistaken in first position, and you are right in all following positions.
Anarchy and Communism are nothing alike, even though there are many anarchist that call themselves communists.
Let me put this in front of you first, because under some measures one could state that the USA is the nation in the world where anarchy has achieved its greatest successes. I hope I don't have to explain this to you, since you support the Libertarian ideal.
As long as you do not see that Liberty and the Lack of Governmental Organization spell A-N-A-R-C-H-Y your head will hurt.
Look in the mirror. You are trying to place something with others as bad, while accepting it for yourself (using a different term) as good.