At one of my classes, some student asked a pretty interesting question: In Orthodox Judaism, can a woman perform brit milah (ritual circumcision)?
A Talmudic Discussion
There is a controversy in the Talmud regarding this very issue between Daru bar Papa who cites in the name of Rav, and Rabbi Yochanan, who differs with Rav. Here is the substance of the argument. Daru b. Papa held that only someone who is obligated to observe the precept of circumcision can act as mohel (the one who performs the circumcision) for others, whereas R. Yochanan felt that a woman can act as a mohelet as indicated in the story of Tziporah (see Exod. 4:24‑26 for details). 
In practical terms, R. Yosef Caro, the Halacha follows R. Yochanan and a woman may act as mohelet  but Maimonides adds one stipulation: this only applies in the event that a male Mohel is not available, however, she is certainly permitted to do so as a religious duty. However, Rema cites authorities who differ on this matter, and discourages a woman from doing acting in this capacity. In fact, the same passage in the halacha states there is no legal obligation on the part of the mother to even circumcise her child, for the duty falls upon the father.
To the best of my knowledge, there is not a single Haredi or Hasidic scholar living today who would literally endorse such a scandalous halachic position. Were such an opinion like this considered halachically normative, many young Jewish men would choose never to get circumcised.
By the way, some rabbinic commentaries assert that Tziporah merely started the act of circumcision on her son, but it was really Moses who completed it.
Adding a Psychological Perspective
From a psychological perspective, the reluctance to utilize a female mohelet may have something to do with Freud’s theory of the “castration complex.” Freud theorized that castration anxiety is based on a deep‑seated fear or anxiety in boys and men said to originate during the genital stage of sexual development; Freud asserts that a boy, when seeing a girl’s genitalia, falsely presumes that the girl had her penis removed probably as punishment for some misbehavior. The young boy then becomes anxious lest the same happen to him.
It is worth noting that in some cultures, notably 19th century Europe, it was not unheard of for parents to threaten their children with castration, or to otherwise threaten their genitals, a phenomenon Freud documents several times.
Freud’s Castration Complex in Patriarchal Religious Societies
Freud’s controversial theory may also help clarify why some Halachic authorities are reluctant to go along with a female mohelet. Freud’s controversial theory may even help explain why male dominated societies like the Muslim and Haredi fundamentalists fear women’s liberation.
The fear that the patriarchal conceptions of masculinity being broken, may explain in part why there exists such an animus directed toward women in these closed societies. Basically, male dominated cultures are fearful of appearing “impotent,” and will do almost anything to promote the image of strength and virility–the trademark of mullahs and Haredi Gedolim (“Giants” ) alike (obviously, another example of Freudian wish-fulfillment, or the Nietzschean “will to power”).
The unraveling of the patriarchal order frightens men, perhaps on a very primordial level. Some scholars suggest that the ascendancy of the patriarchal religions of antiquity was because of their unconscious fear of the goddess religions. Whether this theory is correct or not, remains to be seen. However, it does fit a Freudian castration theory quite well.
A Memorable Story About a Female Mohelet
One of the most moving stories involving a female mohelet occurs in a concentration camp. In Yaffa Eliach’s “Hasidic Tales of the Holocaust,” she narrates an incident at the Janowska concentration camp where, Jewish children were brought (apparently by their parents) from the surrounding areas to be killed.
In her book, one of the great heroes, whose stories she records was that of Rabbi Israel Spira. Years later, he tells the story of what unfolded. “I heard the voice of a woman. “Jews have mercy upon me and give me a knife”. In front of us was standing a woman, pale as a sheet. Only her eyes were burning with a strange fire. I thought that she wanted to commit suicide. … “Give me that pocket knife !” she ordered the German [guard standing by] in a commanding voice. The German, taken by surprise, handed the knife to the woman. … With a steady hand she opened the pocket knife and curcumcised the baby. … “God of the Universe, you have given me a healthy child. I am returning to you a kosher child.” She walked over to the German, gave him back his blood-stained knife, and handed him her baby on his snow-white pillow. Amidst a veil of tears, I said to myself that this mother’s circumcision will probably shake the foundations of heaven and earth.” 
 BT Avodah Zarah 27a
 Yoreh Deah 264:1.
 Maimonides, MT, Hilchot Milah 2:1 By the same token, this was also the view of the Rif (toward the end of his notes in c. Rabbi Eliezer d’milah . . .) as well as the HaGah Maimoni on the Rambam, the Beit Yosef on the Tur Y.D. 261:1. However, the Tosfot rules in accordance with Rav (BT Avodah Zarah 27a, s.v. isha) namely, a woman cannot be a mohelet and this opinion has support in the Hagot Mordechai and the Semak. The same authorities permitting a woman to function as a mohelet, also allow her to recite the traditional blessings said over a brit mila.
 See Freud’s essay “Little Hans” (published in 1909), and “On the Sexual Theories of Children” (1908).
 Yaffa Eliach, Hasidic Tales of the Holocaust (Visalia, CA: First Vintage Books, 1988), 151.