Because the Prophet ﷺ said so, upon him blessings and peace:
1. "Lo! Let absolutely no woman lead a man in prayer!"
"Ala la ta'ummanna imra'atun rajulan."
Ibn Majah, Abu Yaʿla, ʿAbd ibn Humayd in his Musnad, Abu Nuʿaym in the Hilya with different chains from Jabir, and al-Tabarani in al-Awsat from Abu Saʿid al-Khudri.
2. "No nation shall succeed that is led by a woman." Al-Bukhari and Muslim from Abu Bakrah, Allah be well-pleased with him.
This is even more binding in Salat, since the imamate of Salat requires a far more slavish imitation and following than the greater imamate. Further, the imamate of prayer is a delegatory function of the latter.
3. "The best of the men's prayer-rows is the first and the worst the last, while the best of the women's prayer-rows is the last and the worst is the first." Muslim, the Sunan, and Ahmad from Abu Hurayra, Jabir, and Abu Saʿid al-Khudri, Allah be well-pleased with them.
I.e. the contrary of imamate, which means "leading from the front."
4. ʿAli said, Allah be well-pleased with him:
"A woman does not lead as imam." Mudawwana, Iʿla' al-Sunan.
Imam al-Bayhaqi mentioned all the above but the last in his Sunan and said: "This is also the School of the Seven Jurists of Madina among the Tabiʿin then those that followed them."
This is also the position of the Four Schools. More, Ibn Hazm in Maratib al-Ijmaʿ and Ibn Qattan al-Fasi in al-Iqnaʿ fi Masa'il al-Ijmaʿ listed it among the rulings that muster unanimous consensus :
"They concur one and all that a woman cannot lead men in prayer with their knowledge of her being a woman and, if they do, their prayer is invalid by consensus."
Second, it would not be right for one upon whom congregation is not incumbent to lead one upon whom it is obligatory.
Third, the best salat of a woman is in her house without contest, and it is not right that the leader of the Salat be precluded from excellence to begin with.
Both the imamate and khutba belong to those that can lead men in prayer and are subject to the same restrictions.
As for the claim that some of the defunct schools allowed it:
Al-Tabari, al-Muzani, Abu Thawr, and some of the Hanbalis allowed it ONLY in Tarawih AND only if none of the men present knows any Qur'an AND if the woman leads from behind the men's rows - i.e. the contrary of imamate, which means "leading from the front"! See: Ibn Qudama, Mughni; Ibn al-Jawzi, Ahkam al-Nisa'; al-Sanʿani, Subul al-Salam; al-Shawkani, Nayl al-Awtar; al-Tahanawi, Iʿla' al-Sunan; ʿItr, Iʿlam al-Anam.
The preceding paragraph shows that the clause forwarded by Ibn Hazm and endorsed by Ibn Qattan - as cited above - is inexact; more precise is the qualified wording of the vizier Ibn Hubayra (d. 560) in his manual Ikhtilaf al-A'immat al-Arbaʿa:
"They concurred unanimously that the leadership of women over men in Salat is impermissible *in the obligatory prayers*."
This is confirmed by the wording of Iʿla' al-Sunan (4:252), which proceeds to reject the qualification and - rightly - extends the impermissibility to non-obligatory prayers as well. I.e. it is is impermissible across the board.
As for the (weak) hadith of Umm Waraqa in Abu Dawud and Ahmad, then al-Daraqutni's wording has it that the Prophet ﷺ upon him peace allowed her to lead *the women* of her household in prayer. Ibn Qudama, Mughni. Regardless of this specification, the understanding of the Jumhur is that the hadith excludes men. Note that it reaches us through two unknowns, one of them a woman, from Umm Waraqa.
Even if the hadith includes the men, it remains that this dispensation was (a) for non-obligatory prayers only - since men are required to pray obligatory prayers in the congregational mosque - and (b) for the privacy of a single *household,* as further corroborated by the fact that the news of this hadith does not come to us except through unknowns.
Whoever claimed that "ahla dariha" in the hadith means "the people of her neighborhood or village" are ignorant of the Arabic language.(*)
(*) Or the same liars that claimed "a woman named Ghazala led her male warriors in prayer in Kufa after having controlled the city for a day" when the historians only related that when her Khariji husband entered Kufa she went to the mosque and prayed two rakʿats which she had vowed to pray there - alone - in which she recited al- Baqara and Al ʿImran. What should have been far more significant to feminist would-be readers of Islamic history is that the Khawarij gave this Ghazala a share in the spoils of war, IN VIOLATION OF THE PROPHETIC SUNNA with regard to women that took part in the (righteous!) military campaigns of the Companions.
To go back to the hadith of Umm Waraqa:
Since this hadith is the only proof of those that allowed a woman's imamate in non-obligatory prayers, it follows that even so, there is no reliable proof for such a position.
Furthermore, the most knowledgeable woman in creation - ʿA'isha, Allah be well-pleased with her - preferred to pray Tarawih (a) in her house (b) behind a male (c) non-memorizer (d) slave. More, he read from an open mus-haf as he led her and her household in Salat. Muwatta'.
# If there had been a permission for women to lead men in Tarawih, ʿA'isha would have been the first to practice it and, short of practicing it, she would have been bound to communicate it to the Umma. #
Hence, precaution in the fist Pillar of worship dictates that we not leave the established authentic and explicit textual proofs nor the consensus of the mass-transmitted Schools for desperate interpretations of a weak report and the errings of defunct schools and weak positions being cut and pasted by feminists and modernists. And Allah knows best.
Hajj Gibril ©