Because there are so many points that Diamond makes in his book, you will not find any one sentence that sums up his entire thesis. However, there is at least one passage that comes close.
First, let us understand what Diamond is arguing. He is saying that environmental factors caused the great diversity in human societies that we see in modern times. Environmental (not racial or cultural) factors led to the fact that Europeans were able to conquer Native Americans, Australians, etc, rather than vice versa.
There is at least one passage that hints at that overall thesis. It is found towards the end of Chapter 2 (page 65 in the paperback edition), about a page from the end. There, Diamond lists differences between various Polynesian societies and concludes that
All those differences ... developed ... as environmentally related variations on a single ancestral society.
By saying this, Diamond is hinting at his entire thesis. His thesis is that all differences between societies are like the differences between Polynesian socieities. They are all based on environmental factors.