Most diseases are species specific.
Humans don't catch cat flu despite urban legends to the contrary. The majority of diseases pose no threat to humans and can be treated by your doctor. A few are more dangerous to those with poor immune systems and a very small minority are unquestionably dangerous e.g. rabies. Toxoplasmosis is a protozoan which can be spread from cats and a wide variety of other sources to humans. A pregnant woman who contracts toxoplasmosis risks having a baby with congenital defects.