Gemara

67a (Rava): "V'Im Hayo Tihyeh l'Ish (and if she will be Mekudeshes )... " equates the law of the previous Parashah, that a father can annul.

Suggestion: Perhaps the father can annul by himself!

Rejection: If so, why did the Torah need to say "if she vows in her father's house, her father can annul"? If the father can annul (by himself) even when she is Arusah, all the more so when she is single!

68a (Beraisa - Tana d'Vei R. Yishmael): "Bein Ish l'Ishto Bein Av l'Vito (between a man and his wife, between a father and his daughter)" teaches that both must annul the vow of a Na'arah Me'orasah.

Question: What does Rava learn from this verse? (He learned joint Hafarah from "V'Im Hayo Tihyeh...")

Answer: It teaches that a husband annuls vows Beino l'Veinah (that affect their relationship).

70a (Mishnah): If the Arus dies, the father receives authority to annul by himself. In this respect, a father has more privileges to annul than a husband does.

(Rabah): "V'Im Hayo Tihyeh" equates her vows before her second Kidushin to her vows before her first. Just like the father can annul (by himself) before her first Kidushin, also (after she was widowed and) before her second Kidushin.

79a (Mishnah): The following vows may be annulled: vows of affliction, e.g. 'if I will wash...'

79b - Question: He can also annul vows that are not of affliction!

(Beraisa): "Bein Ish l'Ishto Bein Av l'Vito" teaches that a husband can annul vows Beino l'Veinah.

Rishonim

The Rif brings the Gemara verbatim.

Rosh (11:1): The Sifri brings the end of the Beraisa (79b). It says 'we learned that a husband annuls only vows Beino l'Veinah or of Inuy Nefesh. What is the source for a father?' It tried to learn from a Kal va'Chomer, and failed. It concludes "Bein Ish l'Ishto Bein Av l'Vito" equates a father to a husband.

Rambam (Hilchos Nedarim 12:1): A father can annul all vows on the day he hears them. It says "Kol Nedareha ve'Esareha". A husband can annul only vows and oaths of Inuy Nefesh or Beino l'Veinah, e.g. that she will not color her eyes or adorn herself, for it says "Bein Ish l'Ishto."

Question (Chachamei Lunil, brought in Migdal Oz): The Sifri says that also a father can annul only vows of Inuy Nefesh!

Answer (Rambam, brought in Migdal Oz): A Stam Sifri is like R. Shimon. If the Gemara held like him, it would have brought his Drashah. We do not find this Drashah in either Talmud or the Tosefta. Only regarding a husband does the Gemara discuss which vows can be annulled. If we would equate them, why could a father annul matters Beino l'Veinah? He does not care whether or not his daughter paints her eyes, braids her hair ... No Amora discusses which vows are considered between a Na'arah and her father and can be annulled, and which are not. The Torah says that a father can annul "Kol Nedareha ve'Esareha", but a husband can annul only "Le'anos Nafesh."

Rebuttal #1 (Kesef Mishneh): How can we reject a Sifri just because it is not mentioned in the Talmud? We do not find anyone who disagrees with it! The Rambam often rules like a Sifri not mentioned in either Talmud or the Gemara! Even if the simple reading of the verses connotes that a father can annul any vow, a Hekesh equates him to a husband! Indeed, the Yerushalmi (Nedarim 11:1, cited by Ran 68a DH Lomar) equates a father to a husband! Also our Gemara proved that vows without Inuy Nefesh can be annulled from the Beraisa. It expounds "Bein Ish l'Ishto Bein Av l'Vito" to teach that a husband can annul vows Beino l'Veinah. If a father can annul all vows, why did we cite "Bein Av l'Vito"?! The Mizrachi says that the Rambam relies on the Gemara that says 'a father annuls all vows... but a husband annuls only vows of Inuy Nefesh.' There is no such Gemara! The Mizrachi cites the SMaG, and he thought that the SMaG cites the Gemara. The first words of the SMaG cite the Rambam!

Defense #1 (Chasam Sofer Nedarim 79a DH Emnam): The Sifri is like R. Shimon, who expounds Halachos based on the reasons for Mitzvos. A husband can annul only Inuy Nefesh and Beino l'Veinah because those vows she makes conditional on his approval. Presumably, the same applies to a father. This overrides 'Kol". The Halachah does not follow R. Shimon.

Defense #2 (Radvaz Teshuvah 8:149): The Gemara (68a) asked what Rava learns from "Bein Ish l'Ishto Bein Av l'Vito. Rashi says that we asked about "Ish", for it is extra. We answered that it teaches that a husband can annul vows Beino l'Veinah. We did not say so regarding Bein Av l'Vito!

Note: According to Hagahos ha'Bach (3), Rashi explains that the Gemara asked also about Av l'Vito.

Rebuttal #2 (Korban Nesan'el 11:5): The Mishnah (70a) said that the (only) advantage of a father over a husband is that a father receives authority to annul alone after the Arus dies. According to the Rambam, he has another advantage: he can annul all vows!

Rebuttal #3 (Lechem Mishneh): The Gemara (67b) asked, if the father can annul by himself when she is Arusah, all the more so when she is single; no verse would be needed. If he can annul all vows by himself, we need a verse!

Defense #1 (Emek ha'Netziv 2 p.296): The Hava Amina was that a father can annul by himself all vows of an Arusah. The Rambam holds that the Sifri discusses an Arusah.

Me'iri (68a DH v'Havi'uhu): I am sure that an Arusah's father can annul only what the Arus can annul. I am not sure whether the Rambam agrees.

Defense #2 (Keren Orah 68a DH d'Vei): The Rambam rules like Tana d'Vei R. Yishmael, who does not equate a father to a husband from "Bein Ish... Bein Av." Rather, he uses it to teach that both must annul vows of an Arusah.

Rosh (79b DH Melamed): A husband can annul vows Beino l'Veinah, and the same applies to a father. The Gemara discusses a husband, for Inuy Nefesh is written regarding a husband, and we expound to include Beino l'Veinah.

Poskim

Shulchan Aruch (YD 234:58): Some say that also a father annuls only vows of Inuy Nefesh. Some permit (all vows). Some distinguish and say that before Eirusin a father annuls all vows, but if she was widowed from Eirusin and returned to her father's Reshus, he annuls only vows of Inuy Nefesh.

Beis Yosef (DH u'Mah she'Chosav Rabbeinu b'Shem): R. Yechi'el holds that since while she is Arusah, her father can annul only with the Arus, i.e. Inuy Nefesh and Beino l'Veinah (which the Arus can annul), also when she returns to her father's Reshus he can annul only such vows. He did so to reconcile the simple reading of the verses with the Sifri.

Rebuttal (Bedek ha'Bayis): There is no need for this. The Hekesh overrides the simple reading!

Defense (Bach DH Din): When the Arus dies, the father merely inherits his authority. He cannot inherit more authority than the Arus had!

Rebuttal (Gra 111 and Lechem Mishneh, ibid.): The Sifri and Yerushalmi do not distinguish between before Eirusin and when she returned to her father. The Gemara (70b) equates her vows before her second Kidushin to her vows before her first. A Hekesh totally equates the two matters!

Prishah (85): When she was Arusah, the father and Arus could annul together only vows of Inuy Nefesh or between her and both of them. They could not annul a vow between her and her father, or between her and her Arus. The same applies after her Arus died.

Rebuttal #1 (Taz 48): Also a father can annul Beino l'Veinah. The Sifri equates a father to an Arus. A Hekesh totally equates the two matters! R. Yechi'el merely cited the Mishnah, which mentions Inuy Nefesh, but the same applies to Beino l'Veinah. The Rosh explicitly says so.

Rebuttal #2 (Birkei Yosef 8): R. Yechi'el came to reconcile the Gemara with the Sifri, which says that a father can annul vows Beino l'Veinah! It is not clear why the Shulchan Aruch puts R. Yechi'el's opinion last, connoting that it is primary. In Bedek ha'Bayis he rejected it!