In Guns, Germs and Steel, why did writing diffuse or spread from Ethiopia and Arabia from the Fertile Crescent and not from Mexico to the Andes?
The answer to this question can be found at the end of Chapter 12. Specifically, it can be found on pages 237 and 238 of the paperback edition of the book. The basic idea is that geography prevented diffusion in the one case while allowing it in the other.
One of the major ideas of Diamond’s entire book is that geographic luck plays a huge role in determining the fate of a society. It is, for example, the societies that developed agriculture first were those that happened to live in places with many domesticable plants and animals. Similarly, societies that could communicate easily with places that developed writing borrowed writing from its inventors.
Diamond points out that it is relatively easy to get from the Fertile Crescent to Arabia and Ethiopia. All that you have to do is to use the Mediterranean Sea or the Indian Ocean. By contrast, it was very hard to get from Mexico to the Inca Empire in the Andes. As Diamond tells us on p. 238,
Communication between southern Mexico and the Andes required either a sea voyage or else a long chain of overland contacts via the narrow, forested, and never urbanized Isthmus of Darien.
In other words, writing diffused from the Fertile Crescent to Arabia and Ethiopia because it was easy to travel between those places. By contrast, writing did not diffuse from Mexico to the Andes because that journey was very difficult to make.