Am I going to give myself diabetes if I never eat whole wheat?

Not that simple . It depends on your diet as a whole. If you maintain a healthy weight, eat a balanced diet, and have good genes, you can keep your risk of getting diabetes low.
No. Diabetes type i is an autoimmune illness that has nothing to do with diet. Type ii, the one older people get, is dependent on family history and weight. If the lack of whole wheat goes along with a bad diet leading to a sedentary lifestyle and being overweight, then yes. Otherwise no, avoiding whole wheat won't cause any harm.