The answer to this question can be found in Chapter 11, which is entitled “Lethal Gift of Livestock.” As the title implies, Diamond argues having domesticated livestock led to the development of various epidemic diseases.
In relatively primitive farming societies, farmers are typically not very rich. They have relatively poor living quarters. This is relevant because it means that they often live in the same buildings where their animals live at least part of the time. They are also in close contact with the animals quite often. What this means is that any germs that the livestock have will easily be able to transfer themselves from the livestock to the humans. As Diamond says on pages 206 and 207 in the paperback edition of the book,
That transfer is not at all surprising considering that many peasant farmers live and sleep close to cows and their feces, urine, breath, sores and blood.
Diamond then goes on to list a number of epidemic diseases that started out as animal diseases and moved to people. These can be found in Table 11.1. They include measles, tuberculosis, and smallpox. These are some of the most virulent diseases around. They helped to decimate the population of the New World after European contact.
Thus, raising livestock is related to disease because raising livestock puts people in close proximity to animals and allows them to share germs.