Why is it I have to keep away from my dad when he's going through chemotherapy?

Several reasons. I am not sure what has been recommended to you. Secretions and excretions may be hazardous to be in contact with. He may be prone to infections due to the effects of chemotherapy on the immune system. You should ask the oncologist why this recommendation has been made.
Bodily fluids. Chemotherapy can be eliminated from the body in urine, stools, saliva, and sweat. Therefore, during the first 24 to 48 hours, it is prudent not to be in contact with the patient so that you will not get comtaminated with chemotherapy excreted from his body.