Time to play a little bit of catch up, as I have been quiet for a few weeks due to finals. Two weeks ago (sigh) we read Emor. This parasha is full of laws that apply to the purity of the Kohen and the series of Jewish holidays, including the mitzvah of counting the Omer, a period which we are always in when this parasha is read.
The narrative at the end is interesting. A man who is halachically Jewish (his mom is an Israelite from the smallest tribe of Dan) but his father is Egyptian gets into an argument with someone. It is interesting that they refer to one man as "an Israelite man" and the other one as "the son of the Israelite woman".
We define someone as Jewish by their mother, but this is due to gentile soldiers raping our women and causing them to conceive. Would these kids be non-Jewish? Mamzerim (Halachic bastards)? The Rabbis decided that Judaism must go by Maternal Descent so that no matter what happens, the child will be considered Jewish because of the woman. Whereas there are times you may have unanswered questions about paternity, it less likely you would have questions about maternity.
However, in the time of the Torah it seems that it is through the father. This man of Dan is part of the Israelite community but is also an Egyptian due to his father, not a whole Israelite. There are certain people whom Israelite women are forbidden to marry, such as Moabite and Ammonites. Abraham, Isaac, Jacob, Joseph, Moses, etc, marry non-Jews and yet their kids are Jewish. We don't hear of any sort of conversion until Ruth. The position of Karaites is still that of strictly Paternal Descent(see Wikipedia)
And yet the rabbinic Tradition is presented in Mishnah Kedushin 3:12, that is one of confusion and various traditions.
There are reasons for both sides, but I argue that we should maintain the status quo of Maternal Descent. It would create a great rift amongst the Jews throughout the spectrum. Reform and Reconstructionists accept Paternal Descent. Orthodox and Conservagtive only accept Maternal Descent. The change from current Conservative policy would change thousands of years of a general halachic definition of Who's A Jew and would create a further distance between ourselves and the Orthodox. Unfortunately, people are still raped and some people otherwise don't know who is the father of their child and there still can be confusion. I therefore support Maternal Descent to be maintained as the status quo.
For further information please see here ,here, and here.