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.
Psittacosis is an upper respiratory infection usually caught from cage birds e.g. parrots.
It is a chlamydial infection of birds which can cause pneumonia in humans. Although easily cured in healthy adults, it is dangerous to the very young, very elderly and to those with a poor immune system. Psittacosis also causes chlamydial eye and respiratory infections in cats. This a short and simple owner's guide to common zoonoses. If you have any concerns, your veterinarian and your doctor will be able to provide information.