I would like to read material on why jewish descendancy only comes from a Jewish mother or a woman converted according to the Halacha. The tendency today, specially among reform Judaism is that children from a Jewish man married to a non Jewish woman are recognized as legitimate Jews What are the implications?

The source is the Talmud (Yebamot 23a) based on Deuteronomy (=Devarim) ch. 7 verses 3-4. From these verses we learn that if a Jew marries his daughter to a non- Jew (something the Torah forbids), her son is still Jewish and is considered his grandson. If, however, a man’s son marries a non-Jewish woman (also forbidden), their offspring are not considered his grandchildren. The policy of the Reform movement has artificially raised the number of those defined as Jews in the American population while reenforcing the tendency to assimilation.