Milk is usually considered to be very good for you, and it is a good source of protein, fat, and calcium, at least for those children who don't have a milk protein allergy or lactose intolerance. But you can get too much of a good thing.
Infants and toddlers who drink much more than 16-24 ounces of milk each day can have problems with constipation, but the biggest problem is usually all of the extra calories that they are getting from the milk they are drinking. These extra calories usually either cause a child to be full and not want to eat many other nutritious foods and become underweight, or if they are still eating well, then all of the extra calories can lead to their becoming overweight.
Consider that he is drinking 32 to 48 ounces of milk each day, which at 19 calories per ounce, means that he is getting about 600 to 900 calories just from milk. And that is 1/2 to 2/3 of the estimated 1300 calories that a toddler needs each day.
Plus if your child also drinks a lot of juice, he could be getting almost all of the calories he needs from the milk and juice he is drinking, even though that wouldn't provide him with the right mix of fat, protein, carbohydrates, vitamins, and minerals.
Another big problem is that toddlers who drink too much milk are often at risk for iron deficiency anemia. This is usually because milk doesn't have any iron in it, and because if they fill up on milk, then they don't eat many other foods with iron either.
I recently saw a toddler with severe iron deficiency anemia, who ended up requiring a blood transfusion, and the problem ended up being that he was drinking too much milk and not eating enough healthy foods.
(Taken from Vincent Iannelli, M.D.)