A somewhat fragmented text. Some parts are brilliant, other parts would have needed a more active editor forcing the author to tighten up the argument.
By giving many examples from his own research and that of others, Frans de Waal convincingly argues that morality was founded from below, i.e. it began with goal-oriented behavior, via mother-child empathy and further to the constraints that successful collaboration implies in a social species. Our moral sense is not founded on rationality. Which is not to say that rationality cannot have a role in discussing and criticizing morality. The study of primarily chimpanzee and bonobos hints at the how the common ancestor of these species and Homo sapiens behaved, and brings a different light to the behavior of humans. He also weaves in other results from anthropology and the social sciences to show that human behavior has roots and counterparts among mammals and apes more often that is usually realized.
De Waal spends a lot of text attacking the so-called new atheists (Richard Dawkins, Sam Harris, Christopher Hitchens, et al) while at the same time actually agreeing to a lot of what they in fact say. He criticizes Harris for wanting to base morality on science, and distances himself from this view most strenuously, but at the same time bases his own view on morality to a large degree on what the science says. It seems his main bone of contention with the new atheists is that they are vocal and explicit in their critique of religion. His defense of religion is rather tepid; the absence of belief in a moralistic God would create a "vacuum", he contends. As with many intellectuals who use this argument, he himself is an atheist, so apparently that vacuum can't be too bad. He at the same time repeatedly states that morality preceded religion, and that the idea of a moralistic God is most likely a fairly recent phenomenon, at least in the evolutionary timescale. This undermines the idea that religion is vital to our life.