For a study Mullis was working on at the time, he wanted to add a reference to the scientific paper that proved HIV caused AIDS. To his surprise it turned out it simply did not exist.
Later on the medical industry started abusing his PCR invention to "prove" HIV infections. From then until the day he died, he spoke out against it as PCR is incapable of proving infection.
Moreover, Mullis was convinced HIV was not the cause of AIDS.