Things that are antithetic to one another contradict or oppose each other. You might say that eating too many jellybeans at snack time is antithetic to a calm, focused preschool class.
The adjective antithetic is perfect for describing something that clashes with or cancels something else out. Your brother's political beliefs are antithetic to yours if he votes for conservative Republicans while you favor progressive Democrats. And the number of miles your sister has to drive a car each week might be antithetic to her beliefs about conserving energy. The Greek root of antithetic is antithetos, "placed in opposition."