Female rabbis are odd, but not formally prohibited by the Torah. Priests were only male, but rabbinical functions are entirely different, and priestly restrictions do not apply automatically. The Torah precludes females from priestly service, but by the same token the Torah prohibits synagogues as it prohibits any non-Temple houses of worship. One common reason for male-only priestly and rabbinical service is that the sight of women naturally and unavoidably distracts men. Sufficiently old and modestly dressed women might not, theoretically, be a distraction.

Leftist calls for gender equality are irrelevant. Men and women are different, but neither is inferior to the other. At the time when nations sold and rented their wives, Jewish women enjoyed marital contracts; at the time when drunken husbands routinely beat their wives, Shulhan Aruh mandated that a man could not move a finger against his wife and must spend on her and the children more than on himself. Women can be respected but pray separately; that’s no more a discrimination than women’s clubs. The prohibition of common prayers is practical, rather than theological. Jews can object to the reformist practice of mixed-gender services on practical grounds, but it doesn’t contradict the Judaism of the Torah.

Female Jewish scholars enjoy the precedent of Beruria. Women can excel at the loose rabbinical argumentation that largely relies on analogue and allegory. Women often teach in secular universities; they aren’t great scholars, but most male rabbis also are not. Women are good at carefully systematizing data, which is the cornerstone of Talmudic learning.

Women are generally more compassionate than men, an important trait for heads of congregations. Provided that women dress with extreme modesty, pass rigorous exams, and refrain from entering synagogues during niddah, they can be rabbis. Relaxed rules for women’s admittance to synagogues would undermine reformists’ claim to a monopoly on modern Judaism, and attract many mothers to real Judaism.

men aren't priests, either