John Gray nails it; Pinker, as a libertarian with hard Pop Evolutionary Psychology leanings (Gray himself doesn't call Pinker out on that), kind of boxed himself in a corner in "Blank Slate" a decade ago. And, so, "The Better Angels of our Nature" starts out behind the curve.
If people's minds are largely a fixed template, it's hard to explain evolution to non-violence, or lesser violence, isn't it? Of course, Gray does note what I've noted: In the U.S., violence-making has been institutionalized due to the repressive policies of the War on Drugs. And, more interestingly, and more hypocritically, Pinker doesn't object, to the degree he looks at U.S. incarceration rates at all.
He also, as I've noted elsewhere, ignores World War I, WWII, the Holocaust (even using a 1930s European Jewish writer as his starting point) and more.
Timothy Snyder discusses other problems with and failings of the book. To consider violence as strategic, not just hydraulic, a result of societal pressures, means that H. sapiens has great capacity for cynical behavior, among other things. And, it ignores other loads of social science research.
One other brief observation on my part: While Pinker may be right that some people have a Rousellian, or "Gods Must Be Crazy," naivete toward the past, at the same time, he has a Pop Ev Psych "bloody red in tooth and claw" counter-naivete. Fact is that pre-agricultural humans were scavenger-gatherers long before they were hunter-gatherers, among other things that Pop Ev Psychers like to ignore. That issue alone has relevance to the issue of human violence and individual and social psychological malleability.