If you study the history of the matter you will find that this is a latter day development.AI. Definition of Jew
A Jew is a member of an ethnoreligious group and nation originating from the ancient Israelites. Jewish identity is a blend of ancestry, shared history, and cultural or religious practices. People can be Jewish by birth (through a Jewish mother) or by undergoing formal conversion. [1, 2, 3]
Because Jewishness encompasses both ethnicity and religion, one remains a Jew regardless of their level of religious observance or personal beliefs
Originally the line was patrilinear.
Find out what Fruchtenbaum has to say on the matter.