Matrilineal Descent of Judaism

Why is it widely accepted that only those who have a Jewish mother are truly Jewish?

The Torah records Jewish descent as being patrilineal (e.g. from Abraham). Up to first century C.E. it was done this way.

So why did it change? It seems to me that the only proper way to determine if one is truly Jewish by birth is by following the literal examples within the Torah and not the imperfect (probably incorrect) interpretations of a few long dead, Roman-influenced Rabbi.

If it was intended for Jewish descent to be matrilineal, Jews would have been recorded as having been descended from Sarah, not Abraham, and the line would’ve ended after the second generation because they had no daughters.