Fear is one of the most controlling emotions that humans experience. Humans tend to steer away from anything that might harm them, and fear is usually present to alert us about harm. Equality explains in chapter 2,

"There is fear hanging in the air of the sleeping halls, and in the air of the streets. Fear walks through the City, fear without name, without shape. All men feel it an none dare to speak" (46).

People in Anthem exist in fear because of all of the rules that bind them to their daily, monotonous tasks. One rule is that the men live separately from the women. This everyday existence implies that the other half of the human species is off limits, wrong, or bad. Other rules include not thinking for oneself, not living or making choices for oneself, and following a dictated, non-voluntary life schedule--as if a person weren't capable of making such decisions for oneself! The rules cause insecurity and a lack of confidence which voids are only filled with questions of impending doom. When one is not making one's own decisions, a lack of trust can be the result for those who do make the decisions; and, that is exactly how the government wants it. If everyone is paralyzed by fear, then no one will question; if no one questions, then no one learns the truth; if no one learns the truth, then no one will revolt.

In Anthem, why is fear the dominant emotion in society?

One of the reasons why fear is the prevalent emotion of the society that Rand depicts in Anthem is because of its collective nature.  Rand depicts a world where the collective vision must supplant the individualized notion of consciousness.  This becomes difficult because the individual filters through the collective through their own individual lens.  Thus, in understanding the collective, there is an acknowledgement of the individual self, something that is forbidden in the social setting of Anthem:

The word "We" is as lime poured over men, which sets and hardens to stone, and crushes all beneath it, and that which is white and that which is black are lost equally in the grey of it. It is the word by which the depraved steal the virtue of the good, by which the weak steal the might of the strong, by which the fools steal the wisdom of the sages. 

Equality 7-2521 is fundamentally different because he acknowledges his difference.  It is clear that he is fundamentally different than others in the society of Anthem.  He understands his individual difference.  However, much of the social veneer is constructed so that individuals do not commit the "grave" offense of being different. In the desire to be homogenous and to display no distinctive characteristics, there is a fear that permeates everything and all human actions and interactions.  People like Union 5-3992 are part of this collective entity, and individuals must ensure that their compliance and condition of being in the world does not stray from this larger configuration. It is in this light where I think that fear is so dominant in the society where Anthem takes place.  The "EGO" that is so much a part of Rand's heroic protagonist is the very fear of so many in the social order, making Equality 7-2521 that much more a heroic figure.

Why is fear the most prevalent emotion in the society of Anthem?

Anthem is one example in a long series of examples of what is usually referred to as "Dystopian Literature"; that is, literature which depicts the antithesis to the usual Utopian concept of a totally free and progressive society which has eradicated all its crime, disorder, etc. and has evolved into a state of social perfection.

Like Brave New World and 1984, Anthem presents Ayn Rand's view of such a society, which appears to be Utopian, but in reality every aspect of the society is corrupt in some way or other. In almost all dystopian stories (with very very few exceptions) society is controlled by some central oligarchy or a network of nodes of control to keep the members of society from deviating from the expected happy bliss of complete compliance with the rules. In Rand's world, a fragment of post-apocalyptic New York City, the people have been thrown back into a medieval world of intense control. However, as Rand points out in her works over and again, man's liberty and individualism is an end in and of itself, so conformity to rules must always be consensual, not forced. Force is the ultimate violation of the individual, so it is the centerpiece of any dystopia. In this world, fear is ubiquitous and firmly implanted in the minds of the characters. They are several generations removed from the war, so over time have even forgotten to question the authority of the Councils. Like sheep, they follow along and don't resist. The councils and heads of homes are the disciplinarians in the society and are effective in keeping their stranglehold on compliance and conformity with several mottos to support the suppression of individualism and inculcating fear in anyone who might dare to resist.

Thus, fear is a constant tool used by the controlling forces and keepers of the societal mechanism of control and production. Only when the protagonist evolves enough to see his own individuality is he able to begin to act as an individual, face his own fears, and then defy his society's laws. His eventual liberation is a Rand new dawn of life free from institutionalized collective life.

MW