Gemara

28b - Question: Why can a father make his son a Nazir, but a mother cannot?

Answer #1 (R. Yochanan): This law is a tradition from Sinai. (We need not give reasons.)

Answer #2 (Reish Lakish): A father can do so for Chinuch (training in Mitzvos).

Question: If so, a mother should also be able to!

Answer: Reish Lakish obligates a man to train his son, but not a woman.

Question: One should be able to impose even on a daughter!

Answer: He holds that Chinuch applies only to a son, but not to a daughter.

Yoma 82a (Mishnah): We do not make children fast on Yom Kipur, but we are Mechanech them a year or two before adulthood, so they will be used to Mitzvos.

(Rav Huna): We train a child of eight or nine to fast for hours (he eats slightly later than usual). A child of 10 or 11 is Mashlim (fasts the entire day) mid'Rabanan. A 12 year old (girl - some texts omit these words) is Mashlim mid'Oraisa.

Question (Beraisa): We do not make children fast on Yom Kipur, but we are Mechanech them in the Mitzvah a year or two before adulthood.

Answer: This refers to Chinuch of Hashlamah.

Question (Beraisa): What is Chinuch? If he usually eats at two hours of the day, we feed him at three hours... (This shows that 'Chinuch' is not Hashlamah!)

Answer (Rava bar Ula): There are two kinds of Chinuch.

Eruvin 82a (Rav Asi): A six-year old child is Yotzei with his mother's Eruv.

Rishonim

Rif (Yoma 3b): Both girls and boys are Mashlim at 11 mid'Rabanan. We train a child of 10 to fast for hours.

Milchamos Hash-m: Chachamim did not obligate girls to fast earlier than boys, even though they mature earlier, because Chinuch is primarily for boys.

Rambam (Hilchos Shevisas Asor 2:10): We train a child of nine or 10 to fast for hours, e.g. he eats an hour later than usual. An 11 year old boy or girl completes the fast mid'Rabanan for Chinuch in Mitzvos.

R. Mano'ach: The Gemara said that there are two kinds of Chinuch. Hashlamah is Chinuch for the Mitzvah of Inuy, to practice doing it properly. It applies even to girls. Chinuch for hours applies only to boys. It is not a Chiyuv mid'Rabanan. Rather, one must ensure that his sons go on a straight path.

Rosh (Yoma 8:12): We are Mechanech for hours at ages nine and 10, and for Hashlamah at ages 11 and 12.

Question: In Nazir, it says that Chinuch does not apply to girls. In Yoma, it says that we are Mechanech them to fast!

Answer (Tosfos Yeshanim Yoma 82a DH Ben): Only regarding Nazir it is not a Mitzvah to Mechanech them (there is an aspect of sin and repulsion in Nezirus).

Question: Elsewhere, we say that Beis Din need not stop children from sinning. Regarding Yom Kipur, we train them to fast!

Answers (Tosfos Yeshanim): The Re'em says that we are Mechanech to do Mitzvos Aseh, but not to refrain from Aveiros. Fasting is an Aseh (Inuy). The Ri says that Chinuch is a Mitzvah only on the father.

Question: Sukah 2b connotes that Hilni needed to be Mechanech her sons!

Answer (Tosfos Yeshanim): Perhaps they had a father who was Mechanech them. Alternatively, she was Mechanech them even though she was exempt.

Tosfos (Eruvin 82a DH Katan): Even though we are Me'arev only for the sake of Mitzvos, an Eruv helps for a woman's child because she cannot abandon him. Alternatively, it is a Mitzvah to be Mechanech him.

Terumas ha'Deshen (94): According to the Ri, one without a father need not eat in a Sukah if it is difficult. However, the Gemara connotes that Hilni was obligated to be Mechanech her sons, and that they had no father. Tosfos says that it is a Mitzvah to be Mechanech a child in Eruv, even though the Gemara said that the father was not around. Presumably, having a father who is away is like having no father. One should not be lenient.

Poskim

Shulchan Aruch (OC 343:1): If a child is eating Neveilos, Beis Din is not commanded to stop him. His father is commanded to rebuke him and stop him (Rema - from an Isur mid'Oraisa).

Magen Avraham (1): His father is commanded, but his mother is not. We learn from Nazir 29a and from Hilni. Also the Terumas ha'Deshen says so. In Nazir it seems that there is no Mitzvah to be Mechanech a daughter. Tosfos asked from Yom Kipur. Perhaps all Mitzvos are like Yom Kipur, and there is a Mitzvah to be Mechanech daughters. The Medrash supports this.

Question (R. Avraham Yitzchaki, cited in Birkei Yosef 7): Why was the Terumas ha'Deshen unsure about a mother, and leaned to obligate her? It says in Nazir that she is exempt!

Answer #1 (Birkei Yosef): The Terumas ha'Deshen learned from the Re'em. Tosfos said that Reish Lakish says that Chinuch of Nezirus is only for sons, but surely Chinuch applies to girls. Likewise, Reish Lakish exempts a mother only regarding Nezirus. However, he exempted her from training her son 'in Mitzvos', which connotes all Mitzvos. A man must train his son 'in Mitzvos', i.e. all Mitzvos. Presumably, the same applies to the exclusion of a daughter.

Answer #2 (Orach Mishor Nazir 29a and Birkei Yosef): The Gemara said that Reish Lakish holds that Chinuch does not apply to mothers and daughters. This suggests that this is not the Halachah, and that R. Yochanan argues. This is how the Rosh (Chulin 7:17) learned from our Sugya that R. Yochanan forbids Chulin b'Azarah mid'Oraisa. The Halachah follows R. Yochanan against Reish Lakish; this is not one of the exceptions. Rashi (Chagigah 2a DH Ei Zeh) holds that a mother must be Mechanech her son.

Birkei Yosef (7): Maharam bar Baruch says that there is a solid proof from Nazir to exempt a mother. The proof to exempt from Chinuch of girls is less solid, for we train girls to fast on Yom Kipur. The Terumas ha'Deshen challenged the Ri, but Maharam bar Baruch and Hagahos Maimoniyos hold like the Ri, so we follow them, and exempt a mother from Chinuch.

Kaf ha'Chayim (9): Pesach ha'Dvir says that the Mitzvah of Chinuch is only upon the father in his lifetime. After he dies, it is upon his mother and others, even to spend the child's money for Lulav, etc, for surely the child wants this.

Shulchan Aruch (OC 616:2): We are Mechanech a (Rema - healthy) child of nine full years or 10 years to fast for hours, e.g. to eat an hour later than he usually eats. If he is stronger we train him to fast longer.

Magen Avraham: The Ri (Tosfos Yeshanim 82a DH Ben) says that Chinuch is obligatory only on the father. Nevertheless, a mother should not feed her child (who should be fasting for Chinuch) for it is like feeding Isur to him. She may feed him outside the Sukah. There, the food is fully permitted, and she is exempt from making him enter a Sukah. Also, there is a Lav not to eat on Yom Kipur, whereas Sukah is only an Aseh. However, if he takes food by himself on Yom Kipur she need not stop him.

Dameshek Eliezer (6): Rav Huna and Rav Nachman obligate Chinuch of a daughter. We follow them against Reish Lakish. We find no one who argues with Reish Lakish and obligates a mother to be Mechanech.

Mishnah Berurah (5): Some obligate also a mother to train her child.

Rema: The same applies to a healthy girl.

Shulchan Aruch (ibid.): An 11 year old boy or girl completes the fast mid'Rabanan for Chinuch Mitzvos.