Commentaire sur Avot 5:17

THE DISPUTE OF HILLEL AND SHAMMAI. Their students did not fully absorb their ways and teachings, and from that point on disputes became more common among the Torah scholars. This is why the mishna chooses their dispute as an example. Accordingly, the beginning of the mishna does not contradict the end.²³²Just as in the previous mishna, it would seem that any dispute that is not on the same level as a dispute between Hillel and Shammai is not “for the sake of Heaven”. The end of the mishna, however, makes it clear that only a dispute like that of Korach and his followers is considered “not for the sake of Heaven.” Tosafot Yom Tov clarifies that the dispute of Hillel and Shammai is merely an example, and other disputes that are for the sake of truth and not for personal gain would likewise be called “for the sake of Heaven.”

Every argument, etc. [This is] to say about that which it said, "Every argument that is for [the sake of] heaven's name, it is destined to endure" - the intention is that they will endure in their argument forever. And [so,] today they will argue about one thing and tomorrow about another; and argument will endure and continue between them all the days of their lives. And not only this, but [also] 'length of days and years of life will be added to them.'

Hillel and Shammai: Because their students did not serve [in their studies] to their fullest and from them onward, disagreement grew in Israel; therefore it took them for an example. And because of this, there is also no objection from the beginning [of the mishnah] against the end. And see Tosafot Yom Tov.

Every argument that is for [the sake of] heaven's name, it is destined (literally, its end is) to endure: That is to say that the [parties to] the argument are destined to endure and not perish, as with the argument between Hillel and Shammai, [whereby] neither the students of the School of Hillel nor the students of the School of Shammai perished. But Korach and his congregation perished. And I heard the explanation of “its end” is its purpose that is sought from its subject. And [with] the argument which is for the sake of Heaven, the purpose and aim that is sought from that argument is to arrive at the truth, and this endures; like that which they said, "From a dispute the truth will be clarified," and as it became elucidated from the argument between Hillel and Shammai - that the law was like the school of Hillel. And [with] argument which is not for the sake of Heaven, its desired purpose is to achieve power and the love of contention, and its end will not endure; as we found in the argument of Korach and his congregation - that their aim and ultimate intent was to achieve honor and power, and the opposite was [achieved].

Every dispute that is for the sake of Heaven, will in the end endure; But one that is not for the sake of Heaven, will not endure.
Which is the controversy that is for the sake of Heaven? Such was the controversy of Hillel and Shammai.
And which is the controversy that is not for the sake of Heaven? Such was the controversy of Korah and all his congregation.
This mishnah discusses legitimate and non-legitimate disputes. While reading the mishnah we should keep in mind that the Mishnah is the first Jewish book which records disputes between different viewpoints without claiming that one viewpoint is necessarily illegitimate. 150 years before the Mishnah was composed, Judaism had certainly been rife with disputes which caused splinter movements, such as the early Christians and the Dead Sea sect. Part of the overall goal of the Mishnah’s composers was to say that sages can disagree and still live together. We will soon see a classic exmple of this philosophy when we begin to learn tractate Yevamoth.
In Judaism debate is legitimate. Indeed Jews are famed worldwide for being an argumentative people, and this is considered (at least by most Jews themselves) a positive attribute. What is problematic is not debate itself, but debate that does not attempt to reveal the truth, and especially God’s truth. Debate that is only self-serving, an attempt to be victorious over the other side is considered to be illegitimate. The debate that is for the sake of Heaven, which stems from a desire to seek the truth, will endure. The classic example of this are the debates between Shammai and Hillel. This debate endured in several ways. First of all, in the time of the Mishnah, there were probably still scholars who followed Shammai. The debate literally endured, because scholars were still arguing about who is right. Second, students of the Mishnah and Talmud continue to study the debates of Shammai and Hillel. Although by the time of the Talmud law usually follows Hillel, the debate endures as study material throughout the generations.
Korah and his congregation rose up against Moses’s leadership in Numbers 16. Their intent was not a pure complaint against the perceived autocratic style of Moses’s leadership. Rather it was a blatant attempt to gain power for themselves. As our mishnah teaches, it was not a dispute for the sake of Heaven, but rather for their own profit. Therefore, the dispute did not endure, for Korah and his congregation were all wiped out (either by the earth swallowing them or by fire).
Note that the mishnah does not say “the dispute of Moses and Korah”, but rather only mentions Korah and his congregation. This is in contrast to the previous section where both Hillel and Shammai were mentioned. This discrepancy is because Moses and Korah were not operating out of the same motives. Moses disputed with Korah not for his own glory, but for the sake of Heaven. Therefore the mishnah could not mention them together.

THE DISPUTE OF KORACH AND HIS FOLLOWERS. The mishna does not mention the other party in the dispute—Moses and Aaron—as it does in the first section because in this case the two parties are not comparable, for Moses and Aaron acted for the sake of Heaven and had no other motives at all—Midrash Shmuel in the name of R. Yehuda Lerma.

But if it is not for [the sake of] heaven's name - it is not destined to endure: Rather they will cease in their first argument. 'They will end and die there' - as in the argument of Korach.

Korach, etc.: It did not mention the second side of the argument - which is Moshe and Aaron - as it mentioned the two sides in the first [argument]; as here they are not equal. As Moshe and Aaron's intentions were for the sake of Heaven, and there was no aspect in them that was not for the sake of Heaven's name - Midrash Shmuel.