Arguments based on authority are those in which a proposition is claimed to be true because an authority said it is true. As such, it is an obvious logical fallacy because the truth of a proposition is unrelated to what people say about it. Every authority figure ever known has been wrong about things on occasion--some of them quite often. And, the more distant in history an authority is, the more we find that he was wrong about things as science moves forward and discovers actual evidence about the world.
People often believe authorities because we are unable to spend the time and effort to become authorities ourselves on each and every subject in our lives. We rely on authorities on the assumption that they have spent sufficient time and effort investigating the area of their expertise to know what is true or not in that area.
Authorities in theology, however, have nothing to study except the works of other authorities in the field. There simply is no objective evidence to study. That makes theology a classic example of the second reason why an argument based on authority is a logical fallacy. Not only is there no necessary connection between the truth and the opinion of the authority, sometimes people, including authority figures, think something is true because other authority figures said it was--thus causing a circular loop in reasoning.
(This argument is also closely tied to the argumentum ad popularum--the argument that a lot of people believe. They usually believe because an authority told them it was true. Thus the popularity of belief, itself a logical fallacy when offered as proof, is based on yet another logical fallacy.)
Guy P. Harrison's book, "50 Reasons People Give for Believing in God", gives several examples of arguments based on authority:
A sacred book proves my god is real.
Some very smart people believe in god.
Ancient prophecies prove my god exists.
People have gone to heaven and returned.
My religion is so old, it must be true.
Someone I trust told me that my god is real.
When you hear one of these arguments, point out the fallacy and the circular reasoning.
If you hear a citation to holy books or to ancient prophecies:
"Your reasoning is circular. Your holy book and prophecies are meaningful only because you believe; they don't prove the belief to be true."
If the person says that smart people believe or that someone he trusts told him it was true:
"That proves nothing. A lot of very smart people are atheists or belong to other religions. No human knows the truth of such things."
If he claims people have gone to heaven and returned:
"We have no way of knowing if they are telling the truth, had hallucinations or are delusional."
Previously, I mentioned that anyone who claims to know the secrets of the universe's origins is either a liar, a madman or a fool. Well, the one who says he knows because some else told him is clearly the fool because anyone who takes the word of another person for something that no human being can possibly know is obviously a fool.