By exclusively breastfed, do you mean he has only had breastmilk and nothing else (no baby food, cereal, etc.)? If so, it will be a difficult transition. Also, if he has never had a sippy cup it can be difficult.
I breastfed (by nursing and pumped milk in a bottle) my daughter until she was 13 months. However, we introduced the rice cereal and baby food around 6 months. We also introduced a sippy cup with water and juice around 8-9 months I think. At first she hated the sippy cup. We also had to try a few different types of sippy cups before we found one she liked. She was never a fan of juice, but loved water. At 1 year, we introduced cow's milk. She didn't take to it at first. She would take a few sips and that was it. Our pediatrician said not to worry. As long as she was getting calcium from other sources (she loves cheese), there was nothing to worry about. It didn't take long until she warmed up to the idea of drinking cow's milk. Now at 16 months, she will down a sippy cup of milk in no time. It's important to remember that cow's milk is not a substitute for breastmilk or formula. Food is what replaces breastmilk or formula. Cow's milk should be introduced just like any other food. Our pediatrician did say that we could try a little strawberry or chocolate syrup in the milk, but we decided not to go that route. I guess my main advice is just be patient - offer a little at a time, try different sippy cups.
Oh, is it possible that he doesn't like the temperature of the milk? Going from room temperature breastmilk to cold cow's milk can be a change. We sometimes give our daughter the UHT milk that comes in a box (it is sold near the powdered milk). We buy the small boxes and they don't have to be refrigerated (until opened), so it is served at room temperature.