Our Mishna describes the very first disagreement between the Sages: should semikha – leaning on the animal being sacrificed as part of the preparation for the korban, or offering – be permitted on Yom Tov or not? We find no fewer than five generations of Sages listed as arguing this point, which leads Rav Shemen bar Abba to quote Rabbi Yohanan saying that even a shevut – Rabbinic ordinance – must be taken seriously. Semikha involves use of the animal (similar to riding a horse, for example) which is prohibited only on Rabbinic grounds, yet its status on Yom Tov is the topic of discussion for generations.
Aside from the general argument about semikha, we also find a disagreement with regard to women performing semikha when bringing a sacrifice. The Gemara quotes a baraita in which we find that the Tanna Kamma (first) limits semikha to men, based on the passage in Vayikra (1:2) that instructs benei yisrael – i.e. Jewish men – to perform semikha, apparently excluding women from this commandment. Rabbi Yose and Rabbi Yishmael disagree, arguing that women may not be obligated in this mitzva, but they can, nevertheless, perform it on a voluntary basis. Rabbi Yose goes so far as to relate how an animal that was to be sacrificed was brought to the ezrat nashim (Women’s Court) specifically in order to allow the women to perform semikha.
From this Gemara and other similar ones, it appears that according to the Tanna Kamma, not only are women not obligated in the mitzva of semikha – in fact they are forbidden from participating in it. This position can be understood most easily based on Rashi (Rosh HaShana 33a) who rules that whenever a woman does a mitzva that she is not obligated to perform, she effectively transgresses the commandment of bal tosif, which forbids adding to the mitzvot of the Torah. It should be noted that most of the rishonim disagree with Rashi’s position. Tosafot and others explain that, according to the Tanna Kamma, the potential problem is one of marit ayin – that it appears as though the women are engaged in the Temple service, from which they are excluded.