A key thing to understand with regard to anarchists is the nature of our rejection of authority. Cynical naysayers like to jump on this as a way of "proving" that we're a bunch of utopians, saying, "if there's no authority, then there will only be chaos; what if a child ran into a busy intersection? Would you have the 'authority' to intervene, or is that being too authoritarian? If a doctor says I have cancer, am I to reject his opinion on anarchistic grounds?" And so on, ad nauseum.
Anarchists, uniquely, distinguish between legitimate and illegitimate authority. What, then, is the basic test of the legitimacy of authority?
In a society that claims to value the integrity of the individual and the rights of mankind, the only valid test of authority can be: do those who are under a given entity's authority freely agree to be so?
Any authority not based on the free (that is, uncoerced) agreement of individuals and a community of individuals is illegitimate--where such authority is instituted, you will find that force is not far behind. Indeed, force (coercion) is the only thing that can hold such an arrangement together.
Anarchists view direct democracy as the only possible legitimate authority in any society.
Free agreement is the foundation of legitimate authority in anarchism, and this simple question puts the lie to all the existing institutions in our society:
Are any of the bourgeois "democracies" legitimate authorities? NO! The popular mythology is the idea of "government by consent of the governed". How many of you consented to the existing form of government in your given society? Were you asked by those in power? I didn't consent to it--it was there before I was born, and I was born into it. I had absolutely no say in this government. The doctrinal systems of the bourgeois "democracies" work overtime to create the illusion of consent, but what really holds every existing regime "democratic" or otherwise, is not consent, but force.
Is the capitalist workplace an example of legitimate authority? NO! Again, the mythology is that we all "freely agree" to work where we do--the phrasing of it is "you don't HAVE to work for a given boss...you merely choose to." Thus, we are to believe that we do not need to eat, but merely choose to. We work for others (whether employers or clients) because we are forced to, not because we choose to. Moreover, workers in the workplace have no say in what goes on, unions notwithstanding. In fact, the capitalist workplace is the most elitist, and least democratic institution in society today--therefore it cannot help but be fundamentally and absolutely illegitimate!
Anarchists believe the popular self-rule is the only legitimate authority possible in society. Everything else must be maintained through force, which is the antithesis of reason.
And that's really what it all boils down to: force or reason; might or right. All societies in existence today rely ultimately on force, while pretending that the bludgeon really doesn't play a role in bringing about our "consent".
There are only two possible societal models: the society of might, and the society of rights (also known as civil society). The former is based on force, the latter on reason.
It's doubtful that a pure model exists for either, although a fascist society most closely approximates the might-based model, whereas an anarchist society most closely approximates a rights-based model.
Both societies are workable. The question lies in quality of life within each society--in other words, which society would YOU rather live in?
The Society of Might
In the society of might, you are entitled to nothing. You ultimately have no rights, including a right to live. The only way to survive in this kind of society is to scrabble your way to the top; the only bulwark against this world of naked aggression lies in property. With property is security, as property garners wealth and consequently power. So, the goal of the rational person in this kind of society is the acquisition of power. Might-based societies have deeply authoritarian traditions, rigid hierarchies, social stratification, and, naturally, deep disparities of wealth and influence, with property (or lack thereof) determining one's place. And everyone has their place in the society of might--forgetting that will bring swift punishment to the offender.
It's easy to see how the Hobbesian "war of all against all" comes into common practice in this society, and how the emphasis on force and power causes disintegration of the social fabric, making wealth the only effective gauge of worth in a society. It also doesn't take much of a stretch of the imagination to see how closely the "new world order" parallels this model--worse, we are gravitating closer to this model as corporations continue to gain more power. This is not an aberration, but is a natural result of the "triumph" of capitalism--capitalism, despite pretensions to the contrary, absolutely embraces this model, as is more than adequately demonstrated in workplaces around the world in owner - boss - worker relations. The worker's role is to obey the directives of his/her superior.
The Society of Rights
In the society of rights, there is a recognition of what are called human rights. There is a recognition that something called "society" does, in fact, exist. You have a right to live, you have a right to equality and liberty--that is, to be treated as an equal provided you extend this to others in return. In place of force, there is reason; in place of violence, there is cooperation.
Much of what makes our society livable today is the result of hard-won rights garnered by people of past generations. Our "free" society was not granted by governments, but was fought for and won by people like you and me.
What would characterize a rights-based society is an absence of authority and hierarchy, decentralism, community, cooperation, democracy (direct, not bourgeois), and an emphasis on development of the self over acquisition of externalities.
The society of rights would lack property, as property rights ultimately depend on depriving others of the right to live, and thus has no place in anarchist society.
This kind of society exists in pockets, at the local level, but has not prevailed in the face of violence. And that is the one weakness of the society of rights: if you are fighting aggressors who do not recognize your common humanity, you cannot ultimately prevail against them, because they will do whatever it takes to conquer you, up to and including genocide.
This is what happened when the Europeans conquered the world. Not saying that the natives represented rights-based societies--more clearly, I'm saying that European imperialism is a classic might-based societal model, in which a particular way of life was forcibly exported with systematic brutality, in the name of property and profits.
"Survival of the fittest" is how some would term it, equating military success and brutality with evolutionary success--more accurately, in human terms, it should be termed "survival of the fiercest".
Both societal models work; the question remains which you'd rather live within. If you fear taking responsibility for yourself, find cooperation troublesome and don't wish to bother reasoning with others, and find more value in wealth than integrity, then the society of rights is not for you.
If, however, you value liberty, equality, and solidarity, and wish to realize freedom in your lifetime, then the society of rights is the only sane option!
Anarchism is the only theory that recognizes the fundamental wrongness associated with a might-based model of existence, and seeks to bring about a rights-based society through the destruction of coercive relations, as typified by the state and capitalism.