This is because the word milk means young, so young pigeons are also called young pigeons.

Example:

Ruyan drives away weeds. -Bao Zhao's "Singing Mulberry"

Teenagers are like milk tigers. -Qing Liang Qichao's Collection of Drinking Rooms and Anthology

Pigeon refers to the young pigeon within one month before the shell leaves the nest for sale or seed storage. Pigeons are late birds. Young pigeons just hatched can't open their eyes, walk and eat freely, and they can only survive by feeding their parents. The ability of temperature regulation and disease resistance is very poor, so it is the most dangerous period of pigeon's life. At the same time, the meat of young pigeons is thick and tender, which has a strong nourishing effect. Pigeon meat is delicious and tender, rich in nutrients such as crude protein and a small amount of inorganic salts, and it is a rare food.