It's a large part of their culture and religion to trace their ancestry. The only supposedly jewish people that do not trace their ancestry are ashkenazi jews.
If they didn't trace their ancestry they would never know if someone was really their messiah or not (the claimant can only be from the line of David). It's one of the reasons Jesus claimed to be the valid Messiah of the Jews, his maternal ancestry was from a Davidic line. Do you know anything?
