Why did empires, literacy and steel weapons develop earliest in Eurasia and not on other continents?
The answer to this is really the subject of this entire book. Diamond’s major argument is that Eurasia developed these attributes that made it so powerful only by dumb luck. He argues that Eurasia was geographically luckier than other continents.
Diamond argues that farming is what allows societies to become powerful. As he says at the beginning of Chapter 5,
Much of human history has consisted of unequal conflicts between the haves and the have-nots: between peoples with farmer power and those without it, or between those who acquired it at different times.
What he is saying is that the powerful societies are those that develop agriculture first. He says that Eurasia developed agriculture first because it was lucky. This luck led to the empires, the literacy, and the steel weapons that you mention.
Farming allows societies to develop “guns, germs, and steel.” It feeds more people than hunting and gathering. It allows them to become sedentary. It allows some people to do things other than getting food because farmers can grow more than enough for themselves. As this happens, some people can develop literacy because they have the time to do so. Others can create technology like steel weapons. Empires become possible.
Eurasia got these things first because it, as shown in Table 5.1, got farming first. It got farming first because, as Diamond argues in Chapter 6, it simply had the good luck to have many domesticable plants and animals as well as areas with favorable climates. Finally, it had, as he argues in Chapter 10, a long east-west axis along which agriculture could spread.
These factors allowed Eurasia to become dominant.