Why does whether you’re Jewish or not depend on if your mother is Jewish? Why doesn’t the father’s Jewishness count?
First, the biblical inference for matrilineal descent:
“You shall not intermarry with them; you shall not give your daughter to his son, and you shall not take his daughter for your son, for he will cause your child to turn away from Me, and they will worship the gods of others” (Deuteronomy 7:3–4).
The implication is that children from such a union will be torn away from Judaism. Since the verse states “for he (i.e. a non-Jewish father) will cause your child to turn away . . . ,” this implies that a child born to a Jewish mother is Jewish (“your child”), whereas if a Jewish man marries a non-Jewish woman, the child is not Jewish—and as such there is no concern that “she,” the child’s mother, will turn the child away from Judaism.
Although one’s Jewishness is dependent on the mother, other genealogical factors important in Judaism, such as one’s tribal affiliation, are contingent on the father. Thus, whether one is a Kohen, Levite, or Israelite depends on the father’s lineage.
The reason for this is as follows.
There are two basic components to a human being: (a) his essence, and (b) that which he projects forth, such as his talents and abilities. In Kabbalistic terminology, this second component is referred to as “revelations” of himself, as opposed to his essential self.
The creation of a child requires both a man and woman, but for entirely different functions. The mother provides the essence, while the father adds the potential for what the child will eventually project—the revelations of his self.
This is due to the different natures of male and female souls. The male soul emanates from G‑d’s emotive qualities, such as kindness, discipline and harmony—qualities that do not define G‑d Himself, but rather are the means through which He relates to His creations. The female soul, on the other hand, originates in G‑d’s attribute of malchut, royalty. According to the teachings of Kabbalah, malchut is rooted in the essence of G‑d that transcends all divine “revelations.”
The essence of a Jew is his Jewish soul, his Jewish identity. This is inherited from the mother. His tribe—a revelation or projection, the way his Judaism is practiced and actualized—is begotten from the father.
For more on this topic, see our Knowledge Base articles on Essence & Expression; Etzem & Giluyim.