Level 2: Possible reasons for 1st and 3-month-old babies who don’t like to drink milk. 2. How to judge whether the baby is lacking in nutrition. 3. How to make the baby fall in love with drinking milk. 4. What to do if it doesn’t work. 1st-month old baby doesn’t like to drink milk. Possible reasons for breastfeeding For a three-month-old baby, breast milk or formula milk is the main source of nutrition.