My toddler is a bit over 2 and refuses to drink milk from anything but a bottle with a nipple. We have tried everything but my child just won't budge. Once we even went for a week with no milk. My child seems perfectly willing to completely phase out milk to avoid drinking it from a cup, straw, or anything but a bottle. So I have to choose between keeping my child on the nipple and drinking milk or phasing both out. Which is the least bad option for my child?
Will your child drink water from a cup? And does your child like milk-substitute products like cheese, yogurt, etc? If so, you might want to just rely on those. It's never a good idea to turn mealtime into conflict situation. Eventually, your child's memories of drinking from a nipple will fade and you can reintroduce milk. In the meantime, make certain to feed lots of milk products to get proper nutrition.
Drinking from a bottle on an ongoing basis can be quite bad for a child's teeth, causing tooth decay and other problems. On the other hand, cow's milk on a continuing basis is completely optional; your child can get equally high quality protein and fat from meat and calcium from green leafy vegetables. Unless you are talking about pumped breast milk, I would say that phasing both out is the better option.