White blood cells are in your body to protect you from getting sick and so normally they shouldn’t cause disease, however I can think of a couple of things that your question might be getting at!
If you are thinking about HIV/AIDS then this is an infection that actively destroys our immune system!! HIV/AIDS is caused by a virus. It is so dangerous because the infecting virus actually attacks immune cells (white blood cells called CD4 T cells), and so can destroy the immune system – giving people similar symptoms to those born without immune systems. This is what makes it such a devastating illness, and why it is so important to find a cure. In HIV the immune system is being killed directly by the virus though so the white blood cells are not causing the disease.
However acute myeloid leukemia (AML) is a cancer of the myeloid line of blood cells. In this leukemia white blood cells grow abnormally quickly and accumulate in the bone marrow interfering with the production of normal blood cells. AML is the most common acute leukemia affecting adults. Its symptoms include tiredness, shortness of breath, easy bruising and bleeding, and increased risk of infection. Several risk factors have been identified but the specific cause is not known. Because it is acute AML progresses rapidly and is typically fatal within weeks or months if left untreated.
If this was not quite what you meant just leave a comment and I’ll be happy to make it clearer for you! Thanks for the question!! 🙂