My white vanilla cake came out really flat despite using baking powder and soda. My mother told me that the milk (a small glass) I added to the batter may have prevented the cake from rising. Is she right?
No, milk in and of itself does not prevent cakes from rising.
There is noting in milk that changes the action of baking powder or baking soda. Just yesterday, for example, I made chocolate muffins with 1/2 cup of milk, chemically leavened, and they rose beautifully.
There has to be some other factor involved, but you would need to add much more detail to your question in order to have a chance at identifying it.