The answer to this can be found in Chapter 14 of the book. There, Diamond discusses the relationship between food production and the creation of states. He argues that food production (of which domesticating animals is a part) changes the relations between people and helps to lead to state formation.
When people domesticate crops and animals, their societies change. Perhaps the most important change is that the size of the society increases. Before food production, people were largely living in bands whose members were bound to one another by ties of kinship or at least friendship. Once food production begins, however, these ties are loosened. As the size of the population grows, the bonds between members erode. All of a sudden, people are living in close proximity to others who are not kin and may not even be friends. This necessitates a completely new way of living. It creates a need for laws and authority to prevent the unrelated people from (in extreme instances) killing one another.
In this way, domesticating animals (along with other forms of food prodution) increases the size of a society and forces people to find ways to live with unrelated people. This leads to the need for laws, authority and government. This is the beginning of the road to state formation.