The foundational dispute runs through Chazal itself: Mishnah Sotah 3:4 records ben Azzai's view that a father is obligated to teach his daughter Torah so she will understand the laws of the sotah, while Rabbi Eliezer counters that one who teaches his daughter Torah is as if he taught her impropriety (tiflus) — and the Gemara (Sotah 20a–21b) probes Rabbi Eliezer's reasoning, deriving it from the verse in Mishlei that once wisdom enters a person, cunning enters with it.
The exegetical basis for excluding women from the obligation of Torah study is the pasuk Devarim 11:19, which commands teaching 'your sons,' and the Gemara in Kiddushin 29b draws from this that whoever is not commanded to study is not commanded to teach, while Kiddushin 30:1 makes explicit that the verse yields 'your sons but not your daughters.'
The Rishonim codify this framework consistently: Mishneh Torah, Torah Study 1:1–6 states that women, slaves, and minors are exempt from the obligation of Torah study, and the Rambam on Mishnah Sotah 3:4 explains that the mitzva of Torah study applies only to men as derived from 'your sons'; Sefer HaChinukh 419 likewise rules that the commandment applies to males but not females, while noting that a woman who studies Torah does receive reward.
The Shulchan Arukh gives the operative ruling of the classical codifiers: Shulchan Arukh, Yoreh De'ah 246:6 rules that the Sages commanded a person not to teach his daughter Torah because most women are not intellectually prepared and will bring Torah words to frivolity — specifically regarding Oral Torah, which is forbidden, while Written Torah is merely inadvisable but not equivalent to tiflus; the Rema adds that a woman is nonetheless obligated to learn the laws relevant to her own practice.
The Beit Yosef traces these rulings to their Talmudic roots, and Beit Yosef, Yoreh De'ah 246:12 reviews the Rambam's position alongside the Talmudic dispute in Sotah, establishing that a woman earns reward for studying Torah even though her reward is less than that of an obligated man, and that the Sages' prohibition is specifically addressed to the one who teaches, not only to the woman herself.
Several earlier authorities carve out exceptions: Sefer Chasidim 313 distinguishes between the depths of Talmud and the reasons and secrets of Torah — which may not be taught to women or minors — and the practical rulings of the commandments, which a father is obligated to teach his daughters so they can observe Shabbat and other mitzvot; similarly, Magen Avraham 47 notes that women are obligated to learn the laws that pertain to them, as stated in Yoreh De'ah 246:6.
Igros Moshe (YD 3:87) concludes, on our reading of the cited page, that girls in schools such as Bais Yaakov should not be taught Mishnayot, since the Sages forbade teaching Oral Torah to women and likened it to tiflus, but makes an exception for Pirkei Avot on the grounds that it consists of ethical guidance and character development rather than standard Oral Torah content.
Tzitz Eliezer (10:8) is not available in full text for Mekoros to read, but our reading of the cited page indicates that he defends the decisions of recent leading Torah authorities who permitted and established schools to teach girls Torah, arguing that their rulings were necessary to preserve the faith in modern times, and rejects stringent attempts to prohibit all Torah education for girls in the present era.
The question of what may be taught to women in the present generation is addressed directly by B'Mareh HaBazak VII 71:4, which frames the practical question of teaching Oral Torah — including Mishnah — to women today, asking what the position of the poskim is regarding women and Torah study in our times and what subjects are permitted to teach a daughter in the current generation; and Tzitz Eliezer 9:3 concludes, on our reading of the cited page, that a distinction must be drawn between a woman studying Torah on her own initiative — which is permitted and rewarded — and being actively taught by others, and that this resolves an apparent contradiction in the Tosefta which permits women to read Torah and Mishnah.