Besides the general argument that we needed to develop language to make more friends than we could make grooming, Dunbar has some interesting observations that illustrate the breadth of his work. Here are a few:
1. Monkeys developed the ability to eat unripe fruit, dooming the ancestors of apes, chimps, and humans to starvation unless we came up with a response, since we depended on ripe fruit for survival.
Our ancestors' response was to move out of the central forest and into the forest fringe, which made us more vulnerable to predators. We responded to THAT in three ways: selecting for a larger size, forming larger groups, and standing up (which allows better scanning for predators and less exposure to the heat of the sun).
2. There are lots of social species, but to truly form small-group alliances, a species must be able to imagine what other members are thinking--and thus whether a particular other is a reliable friend or likely foe in the intragroup competition for food, safety, ..., etc. Dunbar calls this a Theory of Mind, and says that only primates seem to display it regularly.
Only a Theory of Mind allows for deception ("he thinks that I think, but actually I..."), and possible deception means that there must be a reliable way to build alliances.
3. Females of many species look for an expensive commitment from prospective mates--an elaborate nest, for example, that takes a long time to build. Their implied reasoning is that even if he's tempted to stray, he won't want to go through the hassle of building another big nest. Having to groom your closest friends and allies is the same kind of commitment.
4. Dunbar's grad students have done studies of overheard conversations and newspaper contents, and generally discover that approximately 2/3 of a human communication is gossip about oneself or others.
5. His theory was inspired by the correlation across primate species of group size, clique size, brain size relative to body size, and neocortex size relative to brain size. According to the graphs, the natural human group size is 150 people. (His arguments attempting to prove this hypothesis are interesting, but not among his most convincing.)
This is a fun book, the kind of scientific speculation that lays out a broad theory and invites others to disprove it or come up with something better...