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. Torah precludes females from priestly service, but by the same token the Torah prohibits synagogues as any non-Temple houses of worship. One common reason for priestly and rabbinical male-only service is that naturally and unavoidably, the sight of women 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 not inferior one to another. At the time when nations sold and rented their wives, Jewish women enjoyed marital contract; 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 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 score well in 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 extremely modestly, pass rigorous exams, and abstain from entering synagogues during niddah, they can be rabbis. Relaxed rules of women admittance in synagogues would undermine reformist claim to monopoly on modern Judaism, and attract many mothers to real Judaism.