It’s discussed in the Mishnah/Talmud, in the portion “Kiddushin” (marriages), which derives the law from verses in Deuteronomy, using some pretty involved analysis.
Despite what some say, there is no evidence that patrilineality was ever the standard for who is Jewish. It is simply speculation from the fact that the rule of matrilineality is not explicit in scripture, and the conversion of certain prominent non-Jewish wives (like those of Moses or Solomon) is likewise not explicitly mentioned (though neither can it be definitively said to have not happened).
Noah (the guy with the ark who survived the great flood) was famously a righteous man (the only one in his time! That’s why God saved him);
God gave Noah a bunch of rules , that Noah followed in order to be “righteous”;
Noah wasn’t Jewish (Judaism didn’t exist yet);
Noah was the (male) ancestor of everyone alive;
Noah’s laws have not been cancelled nor superceded, as the other Biblical laws only apply to Jews.
THEREFORE:
The Bible clearly states that a non-Jew can be “righteous” if he or she follows the rules God laid down for Noah;
Hence, a descendent of Noah (that is, anyone) who follows “Noah’s laws” is, by Biblical definition, “righteous”; and
It is not necessary for a non-Jew to convert to Judaism to be righteous.
This partly explains why there is no pressure within Judaism to convert. If you are a believer who believes that adopting a particular faith is necessary for individual salvation, you are more likely to care about conversion (indeed, it would be sort of a crime against your neighbors not to convert them - otherwise good folks who are doomed to go straight to hell if they don’t convert! Nasty!). In Judaism, there exists a standard of “goodness” which, if a non-Jew measures up to it - there is no need for them to convert at all.
Indeed, as I’ve argued before on this board, tribal identity fits Judaism much better than ethnic identity. For one, Jews come in multiple ethnic and racial ‘flavours’ - from white Polish Askenazim to black Ethiopian Beta Israel.
Um, in some cultures it’s traditional after winning a military victory for the soldiers of the victors to rape the women of the losers. You might want to read up on immediately after the Battle of Berlin in 1945.
Well, partly, although, conversion pre-exile is also one of those dubious ideas…there’s a question as to whether or not there was a concept of “conversion” as such. There’s an argument to be made that the wives of Moses and Solomon became Jews/Israelites/what have you, by virtue of the marriage itself.
But it’s also that we see patrilineality in other things. Tribal identity was patrilineal…even today, the son of a Levite father is a Levite, and the son of a Kohen father is a Kohen. That’s strictly in the male line. Also, the monarchy was patrilineal…Solomon became king because he was the son of David, Rehoboam because he was the son of Solomon, and so on, and even today, the Messiah is supposed to be of the house of David. The Northern Kingdom wasn’t so lucky when it came to unbroken succession, but even so, the Moabite stone, which celebrates the revolt of the Moabites against King Ahab, refers to Ahab as of “the House of Omri.”
It’s speculative, but what would make most sense is the notion that the matrilineal standard was adopted at a time when Jewishness was in danger of being diluted, and perhaps completely overwhelmed, by its interactions with powerful neighbouring cultures - perhaps starting during the Babylonian exile? *RivkahChaya suggests in post #18 that . . .
Where it’s men who get to choose wives, rather than the other way around, the matrilineal rule will work to encourage endogamy, and so sustain the identity and continuity of the community at a time when it might otherwise be threatened. As long as the Israelites are defeating their neighbours and taking their women as booty of war, having children with these women is no threat to the community. But once the Israelites are travelling, trading, intermarrying with locals and settling outside territories which are predominantly Jewish, and once they are themselves being defeated and absorbed into larger empires, then intermarriage does become a threat. Hence the development of a norm of matrilineality.
And this would also explain why it becomes such a strong and dominant norm in rabbinic Judaism, which is very much a response to the diaspora that followed the Roman-Jewish wars.
It isn’t unusual for some features to descend through the male line, and others to descend through the female line - today, for example, most Jews accept the naming convention by which children take the father’s last name. The fact that one feature descends through the male line isn’t necessarily proof that all do.