What happens if my dad wants to donate his organs, but I don't want him to?

Discuss it openly. If you are asking the question about deceased organ donation, every individual has the right to declare their wishes while they are alive, and should relate them to their next of kin. In my view, their wishes should be respected and honored. If you have a problem with you father's choices, discuss it directly with him, and have him tell you why he made the choices he made, .
It's Dad's decision. If dad wants to be a donor, he has the right to make that decision. There are others who may influence dad ability to donate. A transplant center is not obliged to accept dad's organs and neither are any potential recipients.