Answer:
   
   The Torah does not always state every law explicitly. In the case of
   Matrilineal Descent, the practice is derived from Deuteronomy 7: 4,
   "Because he will lead astray your son from before Me" To understand
   this verse, look at the preceding verse, which states: "And you shall
   not intermarry with them, your daughter you shall not give to his son
   and his daughter you shall not take for your son". Verse 4 should have
   stated "Because SHE will lead astray your son", for the non-Jewish
   girl that your son married ('your' meaning Jewish) should be the one
   that would lead your son astray. So who is the 'HE'? It might be the
   girl's father, but in general, women leave their father's house and
   live in their husband's house; they would then not be living with her
   father. Hence, it would not make sense for the girl's father to lead
   "your son" astray if your son doesn't live with him.
   
   The Rabbis concluded that 'HE' is the man that your daughter married,
   and 'your son' mentioned in verse 4 is your grandchild, meaning Jewish
   grandchild. Thus, verse 4 is referring back to the middle section of
   verse 3. It reads like this, "your daughter you shall not give to his
   son because he will lead astray your son" This shows that the child of
   a Jewish girl and a non-Jewish boy will be Jewish.
   
   It is not uncommon for the Torah to refer to a grandchild as an actual
   child. For instance, Kings I 15: 11 states, " And Asa did that which
   was correct in the eyes of God just like David his father". David was
   not Asa's father. He was his great-great-grandfather.
   
   Additionally, Leviticus 24:10 speaks of the son of an Israelite woman
   and an Egyptian man as being "among the community of Israel" (ie, a
   Jew). On the other hand, in Ezra 10:2-3, the Jews returning to Israel
   vowed to put aside their non-Jewish wives and the children born to
   those wives. They could not have put aside those children if those
   children were Jews.