Diamond gives one reason why cannibalism was widespread in parts of New Guinea. He gives that reason in Chapter 8, on p. 149 in the paperback edition of the book. On that page, he says
Protein starvation is probably also the ultimate reason why cannibalism was widespread in traditional New Guinea highland societies.
Let us look at why this matters to Diamond’s argument. Diamond’s main argument in the book is that the areas that developed agriculture first (and therefore became powerful) did so because of geographic luck, not because their people were in any way superior to other peoples. He says that some areas simply did not have plants or animals that were good enough to support much agriculture. The highlands of New Guinea are, he says, such a place.
Diamond says that New Guinea had no large-seeded wild grasses that could be domesticated. He says that the root crops that grow in some parts of New Guinea could not grow in the highlands. Finally, he says that there were not large domesticable animal species in New Guinea. Because they did not have any animals or any plants with much protein in them, they were starved for protein. This led them, he says, to cannibalism.