Milk

Milk is one of the seven liquids that cause fruits and vegetables to become "muchshar" (prepared) to receive tumah (ritual impurity), which in Chassidus is compared to the attribute of chesed (kindness), named for its whiteness, sweetness, and clarity. Also on Shavuos, it is customary to eat dairy foods. Milk is also featured strongly in the laws of kashrus.

In Chassidus

In Chassidus, milk alludes to the mochin (intellectual faculties) that emerge from Ima (the supernal mother) and are revealed in Ze'ir Anpin (the emotive attributes). The milk comes out from the breasts, which correspond to the area of the heart, and indicates the illumination of Binah (understanding) which manifests as emotions. Milk is also a metaphor for the waters that nurture the child, meaning the five chasadim (kindnesses) that enter Ze'ir Anpin and develop his middos (emotional attributes) so they become mochin d'gadlus (mature intellect).

For this reason, the Torah is compared to milk, as it is written, "Honey and milk are under your tongue" (this is also the reason for eating dairy foods on Shavuos).

Milk is formed from the woman's blood, as it is taught, "Blood is transformed and becomes milk." Since a woman has five pure bloods and five impure bloods, which correspond to five chasadim and five gevuros (severities), and from the five chasadim, when they rise and are refined at their source, milk is produced that is entirely good.

In the future, Hashem will give Israel to drink from the milk of Torah, as written in the verse, "And it shall come to pass on that day, that the mountains shall drop sweet wine, and the hills shall flow with milk." This will come as a reward for the Jewish people who poured out their souls to death in exile, and engaged in Torah which is sweeter than milk and honey.

Chalav Akum (Milk of non-Jews)

Expanded entry – Chalav Yisrael

This is also the severity of chalav akum, which indicates influence from the side of the klipos (impure spiritual forces).

The Frierdiker Rebbe (Rabbi Yosef Yitzchak) writes about "chalav akum": "Chalav akum and similar things are the weapons of the yetzer hara (evil inclination), which shoot their arrows from afar, and kill Rachmana litzlan (may the Merciful One save us), or make a person spiritually blemished.