Can a woman be a rabbi? This is a complex and multi-faceted question, in part because the role of rabbi contains many different elements and responsibilities, and not every rabbi shares them all. A rabbi can be a community leader, a teacher of Torah, a spiritual mentor, a guide on Torah worldview and philosophy, a ruler on halachic matters, and an adjudicator for monetary and marital disputes.
Now, much of Torah wisdom stems from the Talmud. Since, as we have mentioned previously, the general traditionalist Orthodox Jewish view is that Talmud study is not recommended for women, much of the role of rabbi is by definition unrealistic for them.
Regarding adjudication, there is an additional issue, in that the Talmud says that must be done specifically by men[i].
However, there is another issue here, and that is the gravity of “Mesorah”, or tradition. The Jewish religion was not discovered in a lab or test tube. Our only access to Torah is through its transmission from generation to generation, parents to children, all the way back to the mass revelation at Sinai, which our entire nation was witness to. As such, maintaining the integrity of that transmission is paramount, even with regards to what may seem trivial and inconsequential. For that reason, Orthodox communities strongly reject the notion of female rabbis, even if technically one might be able to argue that it is not always against Halacha.
More questions about the role of women in Judaism? Get your answers.
[i] Yerushalmi Shevuos 4,1. See Tosafos Nidda 49b-50a who discuss how Devorah the prophetess was allowed to judge the Jewish people. See also Rambam Mishna Torah, Melachim 1,5, who maintains a woman should not have any position of community leadership at all. Igros Moshe Y.D. part 2, siman 44 discusses this opinion at some length
By Rabbi Pinchos Fried