In this answer, I will present three main arguments that Diamond makes in Guns, Germs, and Steel that are all pieces of support for his main overall argument. In other words, these three arguments are not the main thing that Diamond is trying to prove in his book. Instead, they are pieces of evidence to prove that main argument.
One argument that Diamond makes is that culture does not determine which groups of people become wealthy and powerful. He says, for example, that Europeans did not conquer Native Americans because the Europeans had a better culture. One piece of evidence for this is found in Chapter 2 of the book. There, Diamond shows that the Maori and the Moriori were both Polynesian people who shared the same original culture. The two groups then split as the Maori ended up in New Zealand and the Moriori in the Chatham Islands. He argues that the Maori became much more powerful and had a different kind of society than the Moriori because the two groups ended up in different environments.
A second argument is that the people who started to farm were those who lived in places with the most domesticable plant species. In other words, people in the Fertile Crescent started to farm before those in North America because they had more plants that they could potentially grow, not because they were culturally superior. One of Diamond’s major pieces of evidence for this is found on p. 140 where there is a table that shows more than half the best grain species in the world were found in the Fertile Crescent. This shows that people there had a much better chance to start farming than people elsewhere.
Finally, Diamond argues that luck explains why some people domesticated animals and others did not. In other words, we cannot say that Europeans domesticated horses because they were better than Africans, who did not domesticate zebras. Instead, Diamond argues in Chapter 9 that the vast majority of animals cannot be domesticated. One piece of evidence is that even Europeans who went to Africa were never able to domesticate zebras. Again, then, it was simply luck that put some people in places where there were animals that could be domesticated.