The answer to this can be found in the Epilogue. Specifically, it can be found on pages 410 and 411 of the paperback edition of the book. As with so much else in this book, the answer is to be found in the geography of the Fertile Crescent and of Europe, which ended up becoming dominant.
Diamond points out on p. 410 that it would be ridiculous to say that the region that we once called the Fertile Crescent is fertile today. That area is now very poor for agriculture. Diamond says that this is because of geographic bad luck. The region was very good for agriculture thousands of years ago. But then people cleared its forests. This led to erosion. Irrigation led to the buildup of salt in the soil. These areas eventually lost their ability to provide food for large populations.
By contrast, Diamond says that the people of northern and western Europe
…had the good luck to live in a more robust environment with higher rainfall, in which vegetation regrows quickly.
Even after Europe has been cultivated for thousands of years, it is still able to support intensive agriculture today. This meant that, as the Fertile Crescent lost its ability to sustain large populations, Europe kept that ability. Population size can often equal power. Therefore, Europe became dominant and the Fertile Crescent became something of a backwater.