(Mishnah): If any of the following Pesulim slaughtered, it is Kosher, even for Kodshei Kodoshim - a Zar, woman, slave or Tamei.

Daf 32a - Contradiction (Beraisa): "V'Shachat" - a Zar, woman, slave or Tamei may slaughter even Kodshei Kodoshim (l'Chatchilah).

Answer: Pesulim may slaughter l'Chatchilah. The Mishnah says that it is b'Di'eved because one of the Pesulim, a Tamei, may not slaughter l'Chatchilah, lest he touch the meat.

Rambam (Hilchos Shechitah 4:4): Anyone who knows the laws of Shechitah and slaughtered in front of a Chacham until he is used to it, he is called an expert. Any expert may slaughter l'Chatchilah by himself, even women and slaves.

Hagahos Maimoniyos (2): This is like the Ri and our other Rebbeyim, and unlike Hilchos Eretz Yisrael, who wrote that women do not slaughter lest they become faint, for Da'atan Kalos (they are light-minded). This is a mere stringency; it is that Chacham's own idea.

Aruch ha'Shulchan (YD 1:37): Da'atan Kalos means that they faint easily.

Magid Mishneh: All Poskim agree that women may slaughter l'Chatchilah. This is clear from Zevachim 31b. The Mishnah does not say that it is b'Di'eved due to women, rather, due to Temei'im, who may not slaughter l'Chatchilah. This is unlike Hilchos Eretz Yisrael. We rely on the Gemara, which permits women l'Chatchilah even for Kodshim.

Rosh (Chulin 1:1): Our Mishnah says that anyone may slaughter. It does not say 'men and women', like it says in Temurah. There, one might have thought that only men make Temurah, for the entire Parshah is in the masculine. Here, a woman is no greater Chidush (that she may slaughter) than a man. In Zevachim, we needed to teach that they may slaughter, because women, even Kohanos, are Pasul for other Avodos. Hilchos Eretz Yisrael says that they may not slaughter l'Chatchilah. Our Gemara is unlike this. If so, we should have said that the Mishnah is Machshir Shechitah of Pesulim only b'Di'eved due to women, which were taught earlier in the Mishnah, and they are b'Di'eved even for Chulin!

Tosfos (Kidushin 76b DH Ein): Slaughtering in the Mikdash is a proof of proper lineage: Women and slaves are Kosher for Shechitah of Kodshim, i.e. b'Di'eved. L'Chatchilah, only people of proper lineage slaughter.

Taz (YD 1:1): The Gemara connotes that only Temei'im are b'Di'eved! Tosfos agrees that letter of the law, Pesulim are permitted l'Chatchilah. Pesulim refrained by themselves. Alternatively, it is an excessive stringency to allow l'Chatchilah only people of proper lineage.

Gra (YD 1:1): Tosfos holds that l'Chatchilah we do not let women slaughter Kodshim. The same applies to Chulin, lest they be negligent.

Tosfos (Pesachim 4b DH Himnuhu): We believe women about Torah laws that they themselves can fulfill, e.g. Shechitah and Nikur (removing Chelev or the Gid ha'Nasheh from beef). Even though they could do Bedikas Chametz, if it were mid'Oraisa we would not believe them, for it is a great exertion that requires great precision. The Yerushalmi says that women are lazy.

Yam Shel Shlomo (Chulin 1:1): Tosfos says that women are believed about Shechitah. This is not because they themselves are believed to slaughter properly. Rather, they are believed to say that it was slaughtered properly, like they are believed about Bedikas Chametz, according to the Yerushalmi that they themselves do not check properly. It is known that Da'atan Kalos, and due to fear of their husbands if they disqualified Shechitah they would hide the matter. Also, perhaps Shechitah was a smaller exertion in those days. Nowadays we have many stringencies, e.g. a pause of any size disqualifies. Tosfos says that they are not believed about any matter of exertion. Or Zaru'a says that we rely on a Shochet to overturn the Isur because most who slaughter are established to be experts. This does not apply to most women, all the more so nowadays after the generations declined. I saw Rabanan refuse to certify youths for Shechitah below the age of 18, based on Hilchos Eretz Yisrael.

Mishbetzos Zahav (YD 1:1): Tosfos says that women are believed about slaughter because they themselves could slaughter! Tosfos Gitin (2b DH Ed (1)) says so even if she does not know how to slaughter, because she could learn. Tevu'os Shor says that she is believed because if she slaughtered, b'Di'eved it is Kosher. This is wrong. If she is not believed mid'Oraisa, even b'Di'eved we do not rely on her Shechitah!

Note: It seems that Tevu'os Shor shows why it is considered that she can fix the matter herself, and therefore she is believed!

Shulchan Aruch (YD 1:1): L'Chatchilah, anyone may slaughter, even women.

Rema: Some say that we should not allow women to slaughter, for their custom is not to slaughter, and this is the custom.

Beis Yosef (DH u'Mah she'Chosav Nashim, citing the Agur): Even though the Poskim hold that women may slaughter l'Chatchilah, the custom in all of Chutz la'Aretz is that they do not. I never saw a custom that they slaughter. One should not start such a custom, for custom overrides Halachah. The custom of our ancestors is Halachah.

Rebuttal (Beis Yosef, ibid.): If they wanted to slaughter and people did not let them, this could be called a proof. Not seeing it not a proof!

Defense (Shach 1): The Agur holds like Maharik (172, brought in Rema CM 37:22), that regarding a custom, if something was not seen, this is a proof.

Beis Yosef (ibid.): Kol Bo says 'Semak says that women slaughter for themselves. This implies that they may not slaughter for men.' This is astounding. What is Kosher for one is Kosher for all! Rather, Semak means that women slaughter by themselves, i.e. without supervision.

Yam Shel Shlomo (Chulin 1:1): I say that 'they slaughter for themselves' means that others may not rely on them.

Aruch ha'Shulchan (37): The Mishnah is Machshir women whom we know do not faint. If one oversees such a woman, surely she may slaughter! In Kodshim, a Kohen is there to receive the blood. Knives in the Mikdash were checked. It is a great exertion to supervise Shechitah of others. Surely, a woman may not be appointed over this! Perhaps this is the Kol Bo's intent.

Mishbetzos Zahav (1): The Rema has two reasons to disqualify women l'Chatchilah. They are suspected of Lifnei Iver (causing others to transgressed), and they often faint. The first reason is dubious, for below (127:3) he rules that women are believed about Nikur beef. One could say that there he refers to Nikur Panim (removing Chelev from the front), which is not a toil. It is better to say that the concern is lest they faint. L'Chatchilah, only someone Muchzak not to faint may slaughter. If women slaughtered, Simlah Chadashah 1:13 says that in a place where they normally do not, we cannot say that most slaughter properly. Where they normally do slaughter, we may let them continue. I say that checking a knife is a great exertion, like Bedikas Chametz, so if we did not check the knife, we do not rely on them. The Rema (Toras Chatas 46:9, and below 127:3) says that if the Isur was established, it is forbidden. Likewise, if she often faints, and says that she did not, she is not believed. Since it is a Safek, she is lenient even if it is not an exertion. We permit her Shechitah b'Di'eved only if she is established not to faint and men checked the knife. One who wants to be lenient may not believe her if she often faints.

Kaf ha'Chayim (8): The Levush says that most women are fearful and faint when they see blood.

Birkei Yosef (4): Most Acharonim say that we do not allow women to slaughter. The Pri Chodosh and Gur Aryeh say that they saw women receive permission to slaughter. Every place follows its custom.

Kaf ha'Chayim (11,12): Our custom is not to certify women to slaughter, even if they are expert and established to slaughter properly. This is in Eretz Yisrael, Surya, Bavel, India, and Persia.

Kaf ha'Chayim (13): If a woman slaughtered, we check if she is expert and says that she did not faint. If she is not here it is Pasul. Because she deviated from the norm, we do not apply 'most slaughterers are experts.'

Kaf ha'Chayim (15): Even where women slaughter, they may not check the knife, for this requires a greatly settled mind and Yir'as Shamayim, more than Shechitah itself.