There are two basic reasons for this fact. First, Eurasia had a greater number of large wild mammal species than any other continent did. Second, fewer large animal species were made extinct in Eurasia than elsewhere. Finally, Eurasia was just lucky to have "good" animals.
In my copy of the book (paperback edition) the first of these facts can be found on p. 162. The second is on p. 163. The third idea is the main point of the whole chapter, but is also on p. 174, which is the next to last page of the chapter.
What Diamond is arguing is that it is much more likely that an animal species will be poorly suited for domestication than that it will be well suited. (There are more ways for a "marriage" to be unhappy than happy.) Eurasia happened to be lucky enough to have a lot of species, many of which were suited for domestication.
The answer to this question can be found in Chapter Nine, entitled, rather intriguingly, "Zebras and Unhappy Marriages." In this chapter, Diamond looks at the number of animals that can be domesticated and how they are scattered over the globe, and also explores reasons why a number of animals can be tamed but can never be domesticated, such as zebras and elephants. Note what Diamond concludes in answer to your question:
Eurasian peoples happened to inherit many more species of domesticable large wild mammalian herbivores than did peoples of the continents. that outcome, with all of its momentous advantages for Eurasian societies, stemmed from three basic facts of mammalian geography, history, and biology.
Firstly, Diamond argues, Eurasia was the geographical location with most diversity, and thus had most candidates for domestication. Secondly, Australia and the Americas actually killed a number of large mammals during their late-Pleistocene extinctions. Lastly, chance decreed that a higher percentage of the animals proved suitable for domestication in Eurasia than in other continents. Thus, Diamond concludes, the combination of these three factors left Eurasia with more domesticable animals than other continents, and thus a massive advantage.