The answer to this question can be found in Chapter 11 of the book. It is near the end of the chapter, on pages 212 and 213 in the paperback edition of the book. Diamond gives two explanations of why New World germs did not kill Spaniards. One is more important than the other.
The less important explanation has to do with population density. As Diamond says
…the rise of dense human populations began somewhat later in the New World than in the Old World.
He also points out that the population centers in the New World were not connected. This makes it harder for infectious diseases to have a large enough population in which to breed.
However, Diamond says a second factor is even more important. He says that the Americas did not have many large animals that could be domesticated. This is very important because Diamond explains in this chapter that the major source of epidemic diseases is livestock. The European diseases like measles and smallpox that devastated the Native Americans passed to people from their livestock. Because there were few domesticated animals in the Americas, there was no source for germs that could have killed the Spaniards.