http://www.infoshop.org/faq/secB1.html

To quote.
First, it is necessary to indicate what kind of authority anarchism challenges. While it is customary for some opponents of anarchism to assert that anarchists oppose all kinds of authority, the reality of the situation is more complex. While anarchists have, on occasion, stated their opposition to “all authority” a closer reading quickly shows that anarchists reject only one specific form of authority, what we tend to call hierarchy (see section H.4 for more details). This can be seen when Bakunin stated that “the principle of authority” was the “eminently theological, metaphysical and political idea that the masses, always incapable of governing themselves, must submit at all times to the benevolent yoke of a wisdom and a justice, which in one way or another, is imposed from above.” [Marxism, Freedom and the State, p. 33]

Other forms of authority are more acceptable to anarchists, it depends whether the authority in question becomes a source of power over others or not. That is the key to understanding the anarchist position on authority — if it is hierarchical authority, then anarchists are against it. . The reason is simple:

“[n]o one should be entrusted with power, inasmuch as anyone invested with authority must . . . became an oppressor and exploiter of society.” [Bakunin, The Political Philosophy of Bakunin, p. 249]

This distinction between forms of authority is important. As Erich Fromm pointed out, “authority” is “a broad term with two entirely different meanings: it can be either ‘rational’ or ‘irrational’ authority. Rational authority is based on competence, and it helps the person who leans on it to grow. Irrational authority is based on power and serves to exploit the person subjected to it.” [To Have or To Be, pp. 44-45] The same point was made by Bakunin over 100 years earlier when he indicated the difference between authority and “natural influence.” For Bakunin, individual freedom “results from th[e] great number of material, intellectual, and moral influences which every individual around him [or her] and which society . . . continually exercise . . . To abolish this mutual influence would be to die.” Consequently, “when we reclaim the freedom of the masses, we hardly wish to abolish the effect of any individual’s or any group of individual’s natural influence upon the masses. What we wish is to abolish artificial, privileged, legal, and official influences.” [The Basic Bakunin, p. 140 and p. 141]

It is, in other words, the difference between taking part in a decision and listening to alternative viewpoints and experts (“natural influence”) before making your mind up and having a decision made for you by a separate group of individuals (who may or may not be elected) because that is their role in an organisation or society. In the former, the individual exercises their judgement and freedom (i.e. is based on rational authority). In the latter, they are subjected to the wills of others, to hierarchical authority (i.e. is based on irrational authority). This is because rational authority “not only permits but requires constant scrutiny and criticism . . . it is always temporary, its acceptance depending on its performance.” The source of irrational authority, on the other hand, “is always power over people . . . Power on the one side, fear on the other, are always the buttresses on which irrational authority is built.” Thus former is based upon “equality” while the latter “is by its very nature based upon inequality.” [Erich Fromm, Man for Himself, pp. 9-10]

This crucial point is expressed in the difference between having authority and being an authority. Being an authority just means that a given person is generally recognised as competent for a given task, based on his or her individual skills and knowledge. Put differently, it is socially acknowledged expertise. In contrast, having authority is a social relationship based on status and power derived from a hierarchical position, not on individual ability. Obviously this does not mean that competence is not an element for obtaining a hierarchical position; it just means that the real or alleged initial competence is transferred to the title or position of the authority and so becomes independent of individuals, i.e. institutionalised (or what Bakunin termed “official”).

http://www.infoshop.org/faq/secA1.html#seca11

Full definition:

The word “anarchy” is from the Greek, prefix an (or a), meaning “not,” “the want of,” “the absence of,” or “the lack of”, plus archos, meaning “a ruler,” “director”, “chief,” “person in charge,” or “authority.” Or, as Peter Kropotkin put it, Anarchy comes from the Greek words meaning “contrary to authority.” [Anarchism, p. 284]

http://www.merriam-webster.com/dictionary/anarchy

2 a: absence or denial of any authority or established order

There’s no such thing as “an anarchist world” — only the idea of anarchy.

“Anarchism is a political theory which aims to create anarchy” — An anarchist world is one that is still attempting to bring about anarchy, which only defines the past and present world.

Furthermore, anarchists aren’t just against some authority or “bad” authority, the very definition and origin of anarchy is “the absence of authority” (an = the absence of, archy = authority), its Greek.

A surgeon is granted authority, but doesn’t need it, they only need the ability to cooperate and work with others in a non-hierarchical based way. No exceptions. The “exceptions” are the boldest oppositions to anarchy. It’s entirely oxymoronic to say there are exceptions.

“Anarchism is primarily a movement against hierarchy. Why? Because hierarchy is the organisational structure that embodies authority.”

If you are going to link to an Anarchist FAQ, its always good practice to read it first…

http://www.infoshop.org/faq/secA1.html

PS — Saying that anarchy or “anarchism” only implies to human animals is an authoritative statement in itself, not to mention downright ignorant in respect to many species that happily enjoy anarchy. But as you do not oppose all authority, this is entirely understandable.