Jewish Status from Mother

See: Mother's Day is Sunday: 18 Signs You Were Raised By A Jewish Mother

Moses was commanded to establish a Sanhedrin as a supreme legal authority (Numbers 11:16). This authority extended to the Sages in each and every generation. The Sages were given authority by Moses in the Torah to make decisions in case of doubt (Deuteronomy 17:8-13). The question that was asked is,
 "Why is it that the Jewish status only passes through the mother and not the father?"
The Sages declared that the Torah is to be understood as saying that Judaism passes through the mother and not the father. There is a Biblical Passage that in Hebrew may be understood grammatically as tracing Judaism through the mother.

Here are the relevant verses as conventionally understood in an English translation.

Deuteronomy (NASB) 7:
 3 Furthermore, you shall not intermarry with them; you shall not give your daughters to their sons, nor shall you take their daughters for your sons. 
4 For they will turn your sons away from following Me to serve other gods; then the anger of the Lord will be kindled against you and He will quickly destroy you.

First of all part of the verse (as per the Hebrew original) should in the singular. Translated more exactly than above it should be read as saying,

Deuteronomy 7:
 3 You shall not marry with them. Your daughter you shall not give to his son. His daughter you shall not take for your son.
 4 For he will turn your son away from following ME....

The key verse in our case is Deuteronomy 7:4.
 It actually says in the Hebrew, "For he will turn your son away from following me." The person denoted here as "he" i.e. the one that does the 'turning away' is "his son" in Deuteronomy 7:3. The one who is turned away is the son of your daughter in Deuteronomy 7:3. The son of your daughter is referred to as "your son" in Deuteronomy 7:4. The son of your son who will have taken his daughter in Deuteronomy 7:3 is not mentioned in Deuteronomy 7:4. In other words the son of his daughter is NOT your son BUT the son of your daughter IS your son.

On the one hand Tribal Status etc passes through the father when dealing with cases within the Nation (Numbers 1:2). National Status however goes through the mother when the parties involved include the Jewish Nation and another.
 No rationale is given. It is a Divine Decree.
Nevertheless a parallel may be found concerning animal species. We are forbidden to yoke two animals from different species together: There is a commandment,

Deuteronomy 22:
 10 You shall not plow with a bull and a donkey together.

This ruling was extended to all animals of different species. It was also prohibited to yoke a horse and donkey together. If you have a mule whose father is a donkey and his mother a horse then you may yoke the mule with a horse. They are considered one species and you go after the mother.
 So too in the opposite direction: If you have a hinny whose mother is a donkey but whose father is a horse then the hinny may be yoked with a donkey BUT NOT with a horse. The mother is the determining element.
(Source: Mishnah Kelaim 8:4).

Post Note: Since the first draft of this posting we received a message thanking us for admitting that matrilineal descent is not written explicitly in the Torah. It is however written. It is NOT merely a Rabbinical decree. Affiliation to the Jewish nation goes through the mother according to the Torah!!! This is what the HEBREW TEXT says! The Hebrew text existed up to 3500 years before the English translations. The English translations may render the text differently because they are not aware of the Rabbinical explanation. At all events these translations cannot be taken as authoritative. The Rabbinical explanation is CONSISTENT with the Hebrew text. In this instance, as in many others, the Oral Tradition and the written message are bound up with each other.