W.M.
I had the same problem with my son. What I ended up doing was waiting a little bit, think about it I drank out of a bottle until I was around 2 1/2 -3. They didn't have sippy cups back then. When he was just over 2 I started by picking the bottle I wanted to eliminate or cut down - the night time one. I started giving him milk in a straw cup (munchin ones are really good) Then I started with his "snack" milk bottle. Once he got good a drinking it out of a straw cup (both water & milk) I did it one bottle at a time. It took 1 month, but now he drinks ALL of this drinks out of a straw cup with no crying over loss of the bottle since I did it gradually. For us the last one to go was the morning bottle. He now happily drinks his milk out of a straw. I recommend starting him with his least important bottle first. Remember to them the bottle is a comfort, so when he used to have his bottles & now has his cup with milk I cuddle him still while he drinks it.