The basic complaint is heard frequently in Conservative and Orthodox circles, namely that the Reform movement has split the Jewish people, because neither the Conservative nor Orthodox branches of Judaism accept patrilineal descent--the idea that Judaism is passed through either parent, not just a mother. It is a fine polemic, but I think it ignores the underlying realities that, to their credit, Reform rabbis are trying to address. I wish that other parts of the Jewish world would also seriously address the issue instead of simply attacking Reform Judaism for facing up to facts.
It is true that matrilineal descent is the rabbinic norm. It's not 5,000 years old, however. The ruling really dates back to the time of the restoration of the Second Temple, to the Book of Ezra--which is more like 2,500 years ago. At that time, with the Jewish people facing the difficult task of rebuilding the Temple, Ezra annulled marriages between Israelites and "foreign wives." Subsequent rabbinic thought builds on this foundation, and that leads us to today.
But if we are talking about tradition, patrilineal descent in Judaism is actually much older than matrilineal descent. Consider for instance that on Friday night in Jewish homes, female children are blessed to be like the matriarchs, while the male children are blessed to be like "Manasseh and Ephraim." This recalls the extraordinary blessing (with crossed hands) that Jacob gives to Joseph's sons.
Joseph lived in Egypt, married an Egyptian woman, and had these two sons. They can only be Jewish through Joseph's side--hence they are Jewish by patrilineal descent, not matrilineal descent. (Perhaps there was a convocation of Reform Rabbis in Egypt at the time?) My point is that while certainly matrilineal descent has been the norm in rabbinic Judaism, it has not "always been the case," as some like to believe. Therefore, in a changing circumstance one can certainly find a biblical basis for patrilineal descent. It's in the very blessing repeated in Jewish homes every week, binding one generation to the next.
What changing circumstance might justify revisiting the issue? According to accounts I've read by Rabbi Alexander Schindler, the head of the Reform movement at the time the decision was made, the issue arose from the plight of Jewish fathers who felt strongly about their Judaism and who wished to pass it on to their children.
In general, Reform rabbis have encouraged conversion before the marriage ceremony. However, the reality was that for many couples, a commitment to Jewish practice arose after children came, not before marriage. The Reform movement recognized that if the children participated in Jewish activities and education, and the family unit as a whole was committed to Judaism, it made no sense to require a conversion ceremony for these children, on the occasion, for instance, of a bar or bat mitzvah. Why add a barrier to Jewish participation by the family members who sincerely wished to participate? In the context of Reform practice, it made no sense to stigmatize a child because the committed Jewish parent happened to be male rather than female.
The insistence on mere biological descent leads to too many obvious absurdities. Yes, it's exciting that some scientists have found "Aaron the High Priest" markers on the Y chromosome of certain Jewish males, but does anyone really want to argue that the genome project is going to uncover a set of Jewish genes? Perhaps it was possible in some previous eras to believe that some mysterious Jewish component was passed on genetically, but can anyone seriously assert that today? No; when we come to assess whether a person is a Jew, we must talk about Jewish souls, not Jewish bodies.