Popa,
That is just one interpretation of what the mishnah in Eduyyot means. The halakha-based Orthodoxy of Eduyyot 2:2 is reiterated by the Beit Yosef Yoreh Deah 1:1, where the Mechaber says that women’s slaughter is not forbidden merely because we haven’t seen it. In fact, a female shochet is Talmudically-authorized by Hullin 2 (haKol Shochtin and Zevachim 31b and 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, citing the same principle I cited from Eduyyot of Lo ra’inu eino ra’ayah). He says explicitly that the claim that it is assur for women to shecht because we don’t see it is wrong. If they wanted to slaughter and people did not let them, this could be called a proof. Not seeing it is not a proof! The Rema holds like the Agur, while the Beis Yosef holds like Eduyyot, which is canonical. Rambam, Hilchos Shechita 4:4, says that 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. The Magid Mishneh here says that 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. We rely on the Gemara, which permits women l’Chatchilah even for Kodshim.