In a lengthy passage (pp 182-184), de Waal applies the not-super-original arguments that "good" is a value judgment, and that increasing the "greatest common good" would devalue and detract from our personal relationships. This is only true when referring to a caricatured, algebraic application of the principal of "greatest common good." De Waal claims that a true striving for the greatest common good would result in an abandonment of our close personal relationships: Why buy your down-and-out brother lunch when there are people literally dying of hunger out there?! And why bring flowers to your Alzheimer's-afflicted mother when you could donate those $30 to Alzheimer's research, to benefit many more people?
In short, this is an argument precariously tiptoeing the precipice of the classic reductio ad absurdum tactic. De Waal is probably correct that if every person subordinated the good of their family for the good of every individual on Earth, personal relationships would be completely empty and meaningless. However, given that postulate and our innate human need for close companionship, that obviously would not be a path toward "human flourishing," and therefore not a valid Utilitarian path. De Waal does a great job tugging at the readers' heartstrings regarding the importance of personal relationships. However, he fails to acknowledge that, assuming his assertions are correct, those personal relationships would be inherently necessary in a Utilitarian "equation." The subordination of personal biases toward one's own relationships for the sake of humanity as a whole is more akin to a Moral Marxism than it is Utilitarianism.