Here is a good explanation...
http://www.beingjewish.com/identity/whoisajew.htmlWho Is a Jew, According to the Torah?How do we define who is a born Jew and who is not? If one of your parents is not Jewish, are you still Jewish?
This subject is a hotly debated one, especially among the non-Orthodox Jewish groups, but I don't really intend to discuss the politics of it very much. I want to simply explain the Orthodox stance, and demonstrate that it is the original Jewish definition.
The original and current Jewish definition of a born Jew is someone whose mother is Jewish. Even though the Torah forbids a Jewish woman to marry a Gentile man, if she does, her children will still be Jewish.
The Torah also forbids a Jewish man to marry a Gentile woman, and if he does, his children by that woman will not be Jewish.
This annoys a great many people who wish to consider themselves Jewish, despite their non-Jewish mother. It is not my intention to annoy anyone. It is my intention to explain Judaism, and not to rationalize any dilution or changes in Jewish Law.
Please understand: if you are in that position, I hear your pain, and I understand and feel it. In no way do I claim that you do not have a Jewish heart, or Jewish feelings, or perhaps even the potential of a Jewish soul. I cannot know these things.
The question of being a Jew, however, is not the same thing, unfortunately. Having a Jewish heart and Jewish feelings does not make someone Jewish. One has to be Jewish according to Jewish Law.
A young woman (I'll call her Sheila) wrote me a while back, complaining about this concept. Her father is Jewish, but her mother is not. She demanded that I prove that the Torah attaches a persons Jewish lineage to the mother. Here are her arguments, and my responses to them.
Sheila wrote me: I am VERY upset to hear that people who are Jewish only by their father's side are not considered by the Orthodox to be Jewish, when in the Torah it firmly states that the father is the leader of the house and all the stories in Torah talked about Jacob, Isaac, Abraham, Moses, etc.
I'm not sure what you mean by "Leader of the house." In any case, there is no indication that the Leader of the household passes along nationality. Tribal affiliation, yes, but not nationality. Let me demonstrate.
Were the Matriarchs Jewish? The answer is yes. (Of course, the word "Jewish" is not exactly the right word to use, since the word "Jew" came about only later, because of the Tribe of Judah, but never mind that for now. "Jewish" is the easiest term to use for this discussion, so we'll use that word.) The Matriarchs, Sarah, Rebecca, Rachel, Leah, Bilha, and Zilpah, were all just as Jewish as Abraham, Isaac, and Jacob.
What made Abraham Jewish? What made Sarah Jewish? Abraham's father and mother were not Jewish. Sarah's father or mother were not Jewish. What made Abraham and Sarah Jewish?
Abraham and Sarah were both Jewish because they converted.
Okay, then why was Isaac Jewish? Was it because his father was Jewish, or because his mother was Jewish? How can you tell? Does it make a difference, if they were both Jewish?
You might ask me, who says that Sarah was Jewish? It's pretty logical that Sarah was just as Jewish as Abraham, but in case you're not convinced, read my article "Was King David Jewish?" You'll find the link below.
For that matter, why wasn't Ishmael Jewish? His father was Abraham. Yet only Isaac became the ancestor of the Jews. Was it because Isaac's mother (Sarah) was Jewish, and Ishmael's mother (Hagar) was not? No, that is not the reason. It was because Isaac chose to serve Hashem, and Ishmael did not.
But according to you, Sheila, since you say that being Jewish is passed along by the father, Ishmael should also have been Jewish. Yet he was not. Apparently, being Jewish was passed along some other way. Was it through the mother? No, it wasn't that either, and I'll prove it.
Let's look at the next generation. Why was Jacob Jewish, when Esau was not? They both had the same mother, and the same father! The reason is because Jacob served Hashem, and Esau did not, and thus Hashem chose Jacob, but did not choose Esau.
All of Jacob's children served Hashem, and therefore Hashem chose all of them.
So we see that the Biblical stories of our ancestors do not show that Jewishness was passed along by the father (or the mother). There is no evidence of that at all.
When we, the children of Israel, stood at Mount Sinai and accepted the Torah, we accepted new Laws that we had never been expected to keep until then. And from then on, Jewish lineage was passed down by the mother, whether or not one accepted Judaism. (And I will prove that below, with Hashem's help.)
As to the stories in the Torah, there are stories of the Matriarchs as well. Our Mother Sarah, exactly like our Father Abraham, was a convert to Judaism. So was Rebecca, because her parents were not Jewish.
So why do most of the stories focus on the men? It is not because they were the carriers of Jewish nationality. It was because the stories that the Torah wants to teach us most often happened with the men. But there are plenty of stories about the women as well.
The stories of the Torah are not there to tell us simply how we are descended from Jews. That is not important, because we can all just convert if we wanted to. Besides, a simple lineage chart would suffice. The stories are there to teach us lessons, not to tell us how we are descended from Jews.
The stories also teach us that we will always carry the merits of our ancestors. Plus they give us object lessons to try to emulate.
Sheila wrote me again: Nowhere in the Torah does it state that only the mother is the passer of the Jewish blood.
And where does it say that the father is? But I shall demonstrate, with Hashem's help, that the Torah does say that the mother carries the Jewish lineage.
When the Torah speaks of the Law against marrying a non-Jew (Deuteronomy 7:3), here is what the Torah says:
Do not intermarry with them; do not give your daughter to his son, and do not take his daughter for your son.
For he will cause your son to turn away from Me, and they will worship the gods of others....
Now, that second verse is strange. The first verse gives the two possible examples: your daughter may not marry a Gentile man, and your son may not marry a Gentile woman. Both are forbidden, and both are mentioned in the first verse.
But the second verse cites only one example. "For he will cause your son to turn away from me...."
Okay, so which example is the Torah talking about? Let's try them in order.
Number 1: Let's say your daughter married a Gentile man. So why does the Torah say "He will cause your SON..." Who is the son? Shouldn't it say "He will turn your DAUGHTER away?"
Okay, so let's try the second possibility: your son married a Gentile woman. Again, why does the Torah say "HE will turn your son away?" It should say "SHE will turn your son away from Me...."
So we need to understand this. Who is this "he," and who is this "son?"
Well, what does the Torah means when it uses the word "son?" Let's look at some examples:
Exodus 2:18. "And they came to their father Re'uel." But they were the daughters of Jethro! (Jethro was also known as Chovev, as we see from Judges 4:11.) Why does the Torah call them the daughters of Re'uel? Re'uel was Jethro's father (Numbers 10:29), and we often find that the Torah calls a grandfather a father, and a grandson a son.
Genesis 20:12. "Furthermore, she is indeed my sister, my father's daughter, though not my mother's daughter, and she became my wife." Abraham was explaining that he had not lied. But was Sarah really his father's daughter? In fact, Sarah was his niece, the daughter of his brother. Therefore, Sarah was the daughter of Terach, her grandfather. So in a sense she was Abraham's sister.
And this is why Abraham told his nephew Lot "we are brothers..." (Genesis 13:8). The grandson of my father is like the son of my father. And that makes him my brother.
Genesis 29:5. Jacob asked the people of the city "Do you know Lavan the son of Nachor?" But Lavan was the grandson of Nachor, not the son of Nachor! Lavan was the son of Besu-el, who was the son of Nachor. In fact, Rebecca, Lavan's sister, told Eliezer "I am the daughter of Besu-el, who was the son of Milkah the wife of Nachor" (Genesis 24:24). So why did Jacob call Lavan the son of Nachor, when Lavan was the grandson of Nachor? Because a grandson is considered like a son.
But is this true of all a person's children? What if you your daughter marries a gentile man, and has a son. Is that child also considered your son?
Well, the Torah seems to say that it is. Where? In the verse we started with, in Deuteronomy 7:4. The Torah says "For he will cause your son to turn away." Who is "he?" Who does it mean by "your son?"
"He" means the Gentile son-in-law. Your son means your daughter's son. Since your daughter is Jewish, her daughter is Jewish. But your Gentile son-in-law might turn your grandson away from Hashem. In other words, if you let your daughter marry a Gentile, your son-in-law will cause your grandson to turn away from Hashem.
But what if it's your son who married a Gentile woman? Well, the Torah does not say "she will turn your son away from Hashem." The Torah does not warn us that the Gentile woman will turn the Jewish man away from Hashem. Why not? I'm not sure, but perhaps it's because if your son marries a gentile woman, he has already turned away from Hashem!
Okay, but what about your son's children? Won't their Gentile mother turn them away from Hashem? The answer is that the children of a Gentile mother are not Jewish in the first place, so the Torah is not worried about them being turned away from Hashem.
To make it clear: why doesn't the Torah say "she will turn your son away from Hashem?" Why isn't the Torah worried that your Gentile daughter-in-law will turn your grandson away from G-d? The answer is because the son of your Gentile daughter-in-law is not Jewish, and he is not considered your grandson (or son) at all.
Sheila asked: Do you decide what G-d accepts??
To which I responded: Of course not. We follow what the Torah teaches.
And Sheila wrote: But, men in power have decided to take away some of the laws of Torah.
And I answered her: But that doesn't make sense. If it were because men wanted power, then they would have given themselves the power of lineage. Instead, according to you they gave the power of Jewish lineage to the women!
Sheila wrote: I want to be Jewish for no other reason except than because I believe it and feel it stir in my heart.
Good, that is a beautiful thing. Then do it the right way. Do it the Torah way.