Why is it important to know how the germs exit the body of a patient?
I think you are referring to knowing how an illness is spread from the patient to others. It is important to know the exact route to how a disease spreads to prevent others from getting infected with the same disease. Unless proper steps are taken based on the knowledge about how germs exit the body of a patient, it could soon turn into an epidemic.
For example, the organisms that cause many illnesses are released from a person's body when s/he sneezes or cough. To prevent these air borne organisms from affecting others, patients should always cover their nose and mouth and those who come in contact with them can use protective masks.
If the germs that cause a disease exit the body through blood, it becomes important to screen blood and ensure that healthcare workers do not come in contact with the blood of those who have the ailment.