What is the source of matrilineal descent in Judaism?
The Mishna (Kidushin 66b) states that if a child’s mother is not Jewish, the child is not Jewish. The ensuing Gemora (Kidushin 68b) explains that this is derived from a verse within the Torah’s prohibition of intermarriage: “And you shall not marry with the non-Jews. Do not give your daughters to his sons; and do not take his daughters for your sons. For he will turn your son away from me and they will worship other gods” (Deut. 7:1-5).
The Talmud notes that the initial prohibition of intermarriage mentions both possibilities, i.e. your daughter to his son, and his daughter to your son. But regarding “turning away”, only “your son” is mentioned, suggesting that “your daughter” is not a concern. But how can that be? Certainly G-d doesn’t sanction a Jewish woman’s turning away! So G-d must have intended a different meaning for the verse.
The explanation depends on who is “he” that will turn “your son” away, and what “son” is being referred to. It can’t mean “he”, your prospective gentile in-law, turning away “your son”, his son-in-law, because if he can turn your son away, certainly his gentile son can turn your daughter away, which is equally unacceptable! Rather the Talmud thus explains that “he” is not referring to your in-law, but rather to his son, the gentile son-in-law married to your daughter, who will turn their children, referred to as “your son” away. However, since only this option is mentioned in the Torah, it reveals that only your grandchild of a gentile man and your Jewish daughter is considered “your son”, i.e. Jewish. But the offspring of a gentile woman from your Jewish son is not considered “your son” but hers, i.e. a gentile.
This explanation is according to the understanding of Rashi and Tosfot Ri Hazaken. The generic Tosfot (ad loc. “Amar krah”) offer other possible explanations of the verse, but all arrive to the same conclusion.
Another source in the Torah is the verse “The son of an Israelite woman went out; and he was the son of an Egyptian man” (Lev. 24:10). Despite the fact that this person’s father is explicitly identified as a gentile, the person himself is referred to by the same verse as being “in the midst of the community of Israel”, i.e. Jewish. The reason is because his mother was Jewish, even though his father was not.
Yet an additional verse for matrilineal descent concerns certain Jews who, returning from the Babylonian exile declare, “We have trespassed against our G-d and have taken foreign wives of the people of the land….Therefore, let us make a covenant with our G-d to put away all the foreign wives and such as are born to them, according to the counsel of the L-rd and of those who assemble at the commandment of G-d; let it be done according to the law” (Ezra 10:2-3). Accordingly, only the children of Jewish men and foreign wives were gentiles; but not children of Jewish women and gentile men.
This law is also found in another Mishna (Yevamot 21a): “One counts as a brother [meaning a fellow-Jew] in every respect [even if his father was a gentile] unless he was the son of an indentured, gentile maidservant or of a gentile woman.” Additional sources are found in Midrash Raba (Nu. 19) and in the Jerusalem Talmud (Kidushin 3:12).
And this in fact is the halacha codified in the Code of Jewish Law (Sh.A., E.H. 8:5) and in Rambam’s Mishna Torah (Forbidden Relations 15:4). There, Rambam states, “This is the general rule: The status of an offspring from a gentile man or from a gentile woman is the same as the status of his mother; we disregard the status father.” Of course, once the mother is Jewish, and the father is also Jewish, then the specific affiliation of the children within the Jewish People is patrilineal regarding whether a person is a Cohen, Levi or Yisrael. When the mother is Jewish and the father is not, even though the children are Jewish, obviously they have no such special patrilineal status since the gentile father has none.