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How do we explain that Bet Shammai is documented as arguing on their teacher Shammai?

I didn't notice any of the classic Meforshim discussing this peculiarity.

There are at least 4 documented cases in Mishnayot:

Eduyoth 1:7:

בֵּית שַׁמַּאי אוֹמְרִים, רֹבַע עֲצָמוֹת מִן הָעֲצָמִים, בֵּין מִשְּׁנַיִם בֵּין מִשְּׁלֹשָׁה. וּבֵית הִלֵּל אוֹמְרִים, רֹבַע עֲצָמוֹת מִן הַגְּוִיָּה, מֵרֹב הַבִּנְיָן אוֹ מֵרֹב הַמִּנְיָן. שַׁמַּאי אוֹמֵר, אֲפִלּוּ מֵעֶצֶם אֶחָד:‏

Eduyoth 1:8 - which is also the end of Ma'aser Sheini 2:4:

כַּרְשִׁינֵי תְרוּמָה, בֵּית שַׁמַּאי אוֹמְרִים, שׁוֹרִין וְשָׁפִין בְּטָהֳרָה, וּמַאֲכִילִין בְּטֻמְאָה. בֵּית הִלֵּל אוֹמְרִים, שׁוֹרִין בְּטָהֳרָה, וְשָׁפִין וּמַאֲכִילִין בְּטֻמְאָה. שַׁמַּאי אוֹמֵר, יֵאָכְלוּ צָרִיד. רַבִּי עֲקִיבָא אוֹמֵר, כָּל מַעֲשֵׂיהֶם בְּטֻמְאָה:‏

Twice in Eduyoth 1:11 - which is also Keilim 22:4:

כִּסֵּא שֶׁל כַּלָּה שֶׁנִּטְּלוּ חִפּוּיָיו, בֵּית שַׁמַּאי מְטַמְּאִין, וּבֵית הִלֵּל מְטַהֲרִין. שַׁמַּאי אוֹמֵר, אַף מַלְבֵּן שֶׁל כִּסֵּא טָמֵא.‏
כִּסֵּא שֶׁקְּבָעוֹ בַעֲרֵבָה, בֵּית שַׁמַּאי מְטַמְּאִין, וּבֵית הִלֵּל מְטַהֲרִין. שַׁמַּאי אוֹמֵר, אַף הֶעָשׂוּי בָּהּ:‏

All the more fascinating that it's in tractate Eduyot, meaning that somebody actively testified as to the veracity of the content of the Mishna in front of a full Bet haMedrash.

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    I think your terminology of "arguing" is somewhat misleading. It's just that R' Yehudah in the Mishnah brings the Braysos (the statements) in their names!
    – Al Berko
    Oct 23, 2018 at 11:54
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    Also "Beyt Shammai" spans over 300 years. Can't the following generations Lechadesh something over their founder? How about R' Eliezer that was also Shmuti (of B"S) - can he say something on his own?
    – Al Berko
    Oct 23, 2018 at 11:56
  • Can this question be expanded to "how far can a student deviate from his Rabbi"? It is a good question. I think that in practice, despite the spiritual Klal of following one's Rabbi, there's no such obligation, moreover, if it is לשם שמים one is compelled to object his Rabbi (Kiddushin 30 something)
    – Al Berko
    Oct 23, 2018 at 12:00
  • In the first case, can't it be that they agree in all cases, but stated the halacha differently - as I believe is often the premise for ukimta s? Maybe the mishna says "afilu" just because Shamai is second.
    – WAF
    Oct 23, 2018 at 13:23
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    @AlBerko Rebbi Eliezer famously refused to say anything of his own. Pick another example.
    – HaLeiVi
    Oct 23, 2018 at 14:53

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This phenomenon is described by R. Shimshon of Chinon in his Sefer HaKeritot (Leshon Limmudim, Sha'ar Sheni, 73).

He suggests that:

ושמא בילדותו תנא להו כמו שאמרו ב"ש וחזר בו בזקנותו והמשנה לא זזה ממקומה.‏

Perhaps he taught to them when he was younger as is stated by Beit Shammai, and then he changed his mind when he was older, but the [original] mishnah was left in place.

So, it's not that Beit Shammai are arguing on Shammai. Rather, Beit Shammai are presenting Shammai's original view, and the view ascribed by the mishnah directly to Shammai is his final position.

He also points out that this would explain why the students' position is presented first, because it was the original view that Shammai arrived at.

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    This is very counterintuitive. You'd think if he'd changed his mind the students' position which persists would be the final one, while the original statement in his name somehow got retained as such and it was tacked on extra at the end because it's just a historical oddity.
    – Double AA ♦
    Oct 23, 2018 at 12:50
  • Beginning of Hazahav has a discussion whether Rebi in his youth or old age was more correct about the kinyan there.
    – user6591
    Oct 23, 2018 at 16:23
  • 1. You should bold the word "perhaps", this seriously weakens the claim 2. If he changed his mind how come he didn't persuade his "Bayt"? This also suggests that he taught what he made up himself, not a tradition he received, which weakens the claim even more.
    – Al Berko
    Oct 23, 2018 at 16:59
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    @AlBerko Again with the downvoting? I’m simply quoting a suggestion of one of the (late) baalei hatosafot. Say that it is a weak/forced answer if you want, but do you really think it’s appropriate to -1 an answer of a Rishon because you don’t find it personally satisfying?
    – Joel K
    Oct 23, 2018 at 17:25
  • I told you, don't take it personally, I admire your ability to find exact sources so fast. What I mean by DW is to mark my judgment if the answer fits/addresses the Q, how complete/extensive it is, how seriously it deals with the problem raised. Because, as I commented, the Tirutz is very weak (in my own eyes) I think it cannot substitute a "true" answer to this question even if 9 other people think so. The fact the Tirutz is uttered by a Rishon does not change anything - it's just a Tirutz.
    – Al Berko
    Oct 24, 2018 at 10:24
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This is in keeping with the Igeret of Rav Sherira Gaon.

The students of both Shammai and Hillel were not on the level of their Masters. As a result, they took different views and quarreling increased. They would sometimes disagree with their Masters teaching.

If you are asking about how they could disagree in practice, meaning wouldn't that demonstrate a lack of respect to their Master?

It was probably after Shammai had passed away. In that circumstance, it is permissible.

The text is silent about when the disagreements occurred.

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