One of the opinions that has become a favorite to pick on in Hilchos Shechita is a sefer called Hilchos Eretz Yisroel by Eldad HaDani (see wiki). The first Tosafos in Chulin quotes Sefer E.Y. as the source to forbid women from shechita because דעתן קלות. Tosafos rejects this opinion by proving from the Mishna in Zevachim that woman are allowed to shecht even kodshim, so they can certainly shecht chulin. The Beis Yosef adds that the explanation of Hilchos E.Y. that they are דעתן קלות simply means that they are more prone to fainting when carrying out the gruesome shechita. Although Tosafos opinion is echoed by all the Rishonim, the Rama (1:1) writes that the minhag is for women not to shecht, which he quotes from the Agur. The Beis Yosef challenges whether there can exist a minhag "not to shecht". Although we have never heard or seen a women shechting, that would not have status of minhag - לא ראינו אינה ראיה. The Shach (1:1) disagrees with the Beis Yosef and says that when something is common and prone to happen, we do say לא ראינו is a proof, because if it was possible to happen, odds are that it would have happened. The Pri Megadim says that there are two reasons that we don't allow women to shecht: 1. they are suspect of violating lifnei iver, 2. they are prone to fainting. Therefore he rules that even bidieved one cannot eat from the shechita of a woman unless their knife was examined carefully and they have a chazaka that they can handle the gruesome shechita without fainting. The Aruch Hashulchan adds an interesting point - since there is a concern regarding the knife that it wasn't examined properly, women wouldn't be able to shecht chulin but would be able to shecht kodshim since the gemara says (zevachim 88) that they would take new knives rather than fixing nicks in the knife. This approach would undermine the proof of Tosafos that if they can shecht kodshim, they can certainly shecht chulin. I found that in the sefer of notes on Rav Eliyahuv's shiurim, he cites a possible source for the minhag that women don't shecht from kiddushin 52b. The gemara says וכי אשה בעזרה מנין, Rashi says that a women wouldn't enter the Azara. Tosafos disagrees because we don't find any issur for a woman to enter the azara. One of Tosafos proofs is that women can do shechita which would require them to enter the azara. Nevertheless, Rashi assumes that the minhag was not to let women in the azara, which could have led to a minhag to not allow women to shecht kodshim. Since they weren't shechting kodshim, it could have extended to chulin as well. The proof Tosafos in Kiddushin cites that women could enter the azara since they are allowed to do shechita is difficult in light of the gemara Chulin 2b that talks about shechting from outside the azara with a long knife (although the gemara is only speaking about using a long knife to prevent touching the animal after it is dead, Tosafos explains that since we are talking about tamei meis, we have to be speaking of a knife that is long enough for him to remain outside the azara and shecht inside the azara ) - women could have done the same.
I wrote a sefer of comments on the Chochmas Adam in Hilchos Shechita. If interested please CLICK HERE.