They tend to be human diseases with no animal reservoir. Once infected, all humans in a population die or recover and the disease disappears. Very closely related diseases are found in these animals. At some point those diseases mutated just enough to become exclusively human diseases. People became infected with animals diseases when there was prolonged close contact between the animals and people.
Diseases represent evolution in progress.
Some zoonotic diseases are animal diseases that only become epidemic human disease if conditions are right. The best historical example is plague, a disease transmitted by rat-born fleas, that wiped out millions of people in the fourteenth century. Incidentally, plague is now endemic in rodents in the western United States. Occasionally domesticated cats pick up infected fleas from the rodent population and an unsuspecting owner catches the disease. Properly diagnosed, plague is readily treated with antibiotics.