The roots of this subject exist in the most ancient discussions of intelligent peoples predating history. The true topic underlying the discussion is really; "How do we co-exist? Do we have rules for the village or does everyone do as they wish?"
I am glad 
Let's look at the meaning of the word.
The origins of the word Anarchy come from the Greek 'anarchos', meaning "no ruler". (Websters Collegiate 10th ed) 1. a: absence of government. b: a state of lawlessness or political disorder due to absence of governmental authority. c: a utopian society of individuals who enjoy complete freedom without government. 2. a: absence or denial of any authority or established order. b: absence of order.
From these individual definitions we get the larger common meaning. 1.a:, 1.b: (being the first) are the most accepted definitions and when used are generally expressed in a negative context; -It's not 'free from law, 'free from government', it is 'absence of', (denoting need). 'Lawlessness' and 'disorder' are certainly not being expressed as positive states.
Definition 1. c: 'a utopian society of individuals who enjoy complete freedom without government.' It's important to know that "Utopia" is the imaginary "ideal country" in the book Utopia by Sir Thomas More written in 1516. In modern common literature, to be "Utopian" is to have impractical and unrealistic ideals or to believe in "impossibly ideal conditions". The word Utopia is actually used to mock unrealistic or fantasy-based social concepts.
Now, here's the real problem with Anarchy as found in definition 2.a:; "...denial of ANY authority or established order". Any person proclaiming to be an anarchist needs to consider the true meaning of this. This is the over-sweeping context recognized as Anarchy and puts it at odds with any functioning culture or society on Earth. The reasons for this should be self-evident. Consider this; Your physical body is recognized as "established order". You are the "authority" within that body. One's home is "established order", the occupant is the "authority".
Nothing in the idealism of Anarchy recognizes or protects this very important element. This Natural Law. In fact, the essence of Anarchy completely denies it. In the simplest context "No established order" and "the denial of any authority" are obviously not viable solutions for coexisting peacefully with each other. Anarchy by it's own definition is anti-structure, anti-culture and anti-social. I suggest activists pick a different word with a better meaning to express one's ideals with. You might as well be waving a huge flag with a big brown blotch in the middle and little 'stink lines' emanating from it.
Just to be clear, I am very experienced with Anarchy.
I personally have had direct and very extensive interactions with well established and recognized Anarchist groups here in Denver. Especially during Occupy Denver. I watched as the idealism of "No order" and "No leaders" devolved the efforts of an intelligent and organized community of rational people into a completely confused, disorganized, suspicious and ineffective mob of misplaced intentions. This pliable mob was then easily manipulated toward violent confrontations with authorities that should have never happened.
The Anarchists, though espousing 'no order', were very well organized. They controlled the public website as well as the assembly meetings. They implemented the Hegelian Dialectic of "Problem-Reaction-Solution" by leading and encouraging participants to break the law, which of course brought armored state thugs down upon the assembly who then injured and arrested many people. These televised events discredited all efforts of the assembly from that point on. The 'solution' then presented was collecting roughly 30k from the general assembly to pay for legal assistance. This resulted in many of their own friends and members being released and then, surprise surprise, over $9000 went missing. Several people that followed the Anarchists were left in jail. There were people who spent over 1 year incarcerated and to this day still have legal issues.
I also personally watched these same concepts of "no order" and "no authority" completely infiltrate, take over and dissolve one of the most important and influential We Are Change chapters in the world. This idealism was promoted outside of meetings and without group discussion or awareness. It spread like a virus and regardless of my efforts it devolved many years of hard work, organization and successful action into mistrust, chaos and complete ineffectiveness. Just like the program intended. I had no choice but to leave the organization as did the majority of long-standing veteran members.
We have to ask ourselves, can a healthy social environment exist without some form of order? All historical evidence reveals it cannot. A healthy communal system cannot sustain in chaos and disorder. I have literally met many people that sincerely believe the world as portrayed in "Mad Max" would really be great. I assure you with deadly seriousness, it would not.
In a simpler perspective closer to practical life, how does Anarchy work within our own homes? Do the kids just get to do whatever they want? Is it NECESSARY to have some form of structure in a household? Who upholds that structure? That's right, Grandma is the authority, Mom and Dad are the authority. The ones that have the wisdom and experience guide the ones who do not. This is the essence of FAMILIA. It is the natural and true foundation of community.
Regardless of opinion, community requires the agreement of all individuals involved to accept and follow certain rules and guidelines set forth by the collective. Yes. It requires Law. If you observe any form of Nature, you will see that it follows natural laws. Being symbiotic of that same Nature, we also follow these laws. Contrary to popular belief, The Rainbow Gathering exists by rules and laws. Any social gathering or organization cannot escape it.
A question I have is why align oneself with a pre-made concept advocating the 'absence of order' instead of something positive? Why choose the word Anarchy as a flag to wave? Why not Familial Culture, Communal Cooperation etc. Why not just recognize and support the success and good nature that already exists within our own society? It is not perfect by any means, but amazingly we are doing pretty well considering everything we have been through. Anarchy as I have repeatedly seen it, has the absolute red flags of a Covert Intelligence Program, and it always has. Recognizing and understanding "social engineering and covert operations" is one of my specialties. The evidence is everywhere. Believe me, it's way too obvious to deny that modern Anarchy is Co-Intel-Pro. A planned and organized system of counter-intelligence-provocateurs.
The word Anarchy has a globally accepted association deeply programmed into our collective minds. One of those programs is the image of Johnny Rotten & Sid Vicious shouting Anarchy between spurts of drug induced violence and disfunction. This ideal of Anarchy was one example laid before the youth of that era. This concept was just nihilism in disguise, and of course, the youth of the era ate it up like candy. Millions fell to drug overdose and social violence emulating this "popularized ideal".
To this day I enjoy the "Sex Pistols" music, but I also recognize the program. Sold as rebellion against British totalitarian control, it's true effect created an "enemy culture" and then created complete disorder within that culture so it cannot manifest positive change. The sad truth is that as soon as you say the word Anarchy, this is the association that will immediately arise in the majority of educated people. -Not to mention the array of violent images fed through the media over the last 50 years directly associated to the word "Anarchy". This word is NOW A PROGRAM within the western mind. If you know anything about psychological conditioning, just the word alone triggers the cerebral cortex's automatic response system to engage the lymbic emotional response towards fear and aggression.
In simple English, the word Anarchy translates into "social disorder". By the simplest laws of nature, disorder immediately becomes dysfunction. No matter what you want to think about it, we must accept that community is founded on order. This is the pattern and nature of the human intellect. Math is order. Music is order. The ability to control our thoughts and reactions and consciously create with intention is order. This is what separates us from the animal world. I mean, I love animals but I do not wish to return to that state and live under animal law.
From all evidence, Human intellectual patterns are themselves the very essence of "order". The nature of order is functionality, harmony, cooperation, ..sustaining patterns. Anarchy does not in any way promote these ideals. Websters definition of an Anarchist is: "One who believes destruction of society is preferable to the present state." Disorder and destruction. What a kind, loving and absolutely glorious vision for Humanity.
Another red flag that screams "Social Engineering" is the fact that Anarchy offers no solution for building or guiding society after the destruction phase. (anybody else notice this?) Where is the plan, what is the ideal? If a plan ever does emerge I will show you the essence of government within that plan.
As long as one uses the word Anarchy, the endeavor becomes "ANTI", instead of "PRO". When communicating the concept of Anarchy to others, we lose them in the diffuse nature of a word and are no longer expressing or creating a true ideal. This word is a program created by Tavistock and the CIA. The only way to counter the program is to get away from the word. Keep to the deeper ideals of freedom and personal responsibility that exists beyond the artifice.
Then you won't need a word to categorize and confine your true nature.
~X