Have asked a few questions, this is what I got.
It's been said that Judaism is "more like a nationality than like
other religions," because traditionally, a person must be born
Jewish or go through a lengthy conversion process. The strictest
definition of a Jew is one whose mother was Jewish.
This doctrine of matrilineal descent has been part of Judaism since
at least the second century C.E. (common era), when it was codified
into the Talmud, the body of religious writings that supplement the
Jewish holy book of the Torah. The Talmud expands on the Torah
passages of Deuteronomy 7, which oppose intermarriage by Jews. This
verse states that the child of a Jewish woman and a non-Jewish man
will be Jewish. Other Torah verses admonish Jewish men from taking
non-Jewish wives because their children will not be Jewish.
Why and how matrilineal descent evolved is unclear. Other aspects
of lineage, such as one's affiliation with the Jewish tribes, are
traced through the father. And in the Hebrew Bible, paternal
lineage often plays a more important role. Scholars have suggested
various reasons for the use of maternal lineage in determining
Jewish status.
For one, a child's mother is always known, while the father
couldn't be positively identified before modern technology. Also,
the Jewish people suffered a long history of oppression, during
which Jewish women were sometimes raped by their oppressors.
Instead of casting out the woman and the child born of the rape,
the Jewish community took them in by considering the child to be
Jewish.
Responding to the rise of intermarriage among American Jews, the
Reform movement of Judaism took the radical step of redefining who
is considered Jewish. The Central Conference of American Rabbis
declared that the child of one Jewish parent, mother or father, is
presumed to be Jewish. However, children of mixed Jewish parentage
should establish their Jewish identity through Torah study and
public, formal acts such as a Bar/Bat Mitzvah. This Reform position
is controversial among Jews and not typically recognized in Israel
today.