Why Does the Jewish Law(Halacha) Define A Jew Only By Matrilineal Descent?

To put it briefly, it is because of the role the mitochondria, which is chiefly maternally inherited, play  in genetic evolution. Evolution takes place in two phases: the hidden phase and the emergent phase. The hidden phase occurs over hundreds or even thousands of generations within the mitochondria. Throughout this period, no physical change can be observed in the organisms.
Then at the emergent phase, changes are communicated from the Mitochondrial DNA to the nucleus which houses the nuclear DNA. The nuclear DNA metamorphose accordingly.
This emergent phase takes place within a generation. Learn more [here].
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