Just curious as to why you feel the need to drop the bottles?
You could slowly decease how much he has over the course of a month or so and work to add that calcium intake elsewhere. Neither of my boys drink as much milk from a cup as they did from bottles, that's a lot of milk! They do however, eat many calcium rich foods and a very healthy diet, so I'm not concerned about intake from a cup.
Looking at the broader picture you might determine a.) it's not critical now to lose the bottles, but decrease them over time to achiever your goal. b.) work to make up the lost milk in other ways if you're not confident the milk will be consumed from a cup.
Probably if he's having a hard time letting go of the bottles he's not ready to do so yet and is trying to tell you with his reactions. A gradual approach, I've found in my experiences, to work much better with my boys and I also like that I'm respecting their needs when going about it gradually.
Just a different approach to consider -- may or may not be right for your family.