זִכָּר֞וֹן לִבְנֵ֣י יִשְׂרָאֵ֗ל לְ֠מַעַן אֲשֶׁ֨ר לֹֽא־יִקְרַ֜ב אִ֣ישׁ זָ֗ר אֲ֠שֶׁר לֹ֣א מִזֶּ֤רַע אַהֲרֹן֙ ה֔וּא לְהַקְטִ֥יר קְטֹ֖רֶת לִפְנֵ֣י יְהוָ֑ה וְלֹֽא־יִהְיֶ֤ה כְקֹ֙רַח֙ וְכַ֣עֲדָת֔וֹ כַּאֲשֶׁ֨ר דִּבֶּ֧ר יְהוָ֛ה בְּיַד־מֹשֶׁ֖ה לֽוֹ׃
....It was to be a reminder to the Israelites, so that no outsider—one not of Aaron’s offspring—should presume to offer incense before the LORD and suffer the fate of Korah and his band.
ולא יהיה כקרח. כְּדֵי שֶׁלֹּא יִהְיֶה כְקֹרַח:
ולא יהיה כקרח means in order that he be not as Korah.
כָּל מַחֲלֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, סוֹפָהּ לְהִתְקַיֵּם. וְשֶׁאֵינָהּ לְשֵׁם שָׁמַיִם, אֵין סוֹפָהּ לְהִתְקַיֵּם. אֵיזוֹ הִיא מַחֲלֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, זוֹ מַחֲלֹקֶת הִלֵּל וְשַׁמַּאי. וְשֶׁאֵינָהּ לְשֵׁם שָׁמַיִם, זוֹ מַחֲלֹקֶת קֹרַח וְכָל עֲדָתוֹ:
Every argument that is for [the sake of] heaven's name, it is destined to endure. But if it is not for [the sake of] heaven's name -- it is not destined to endure. What is [an example of an argument] for [the sake of] heaven's name? The argument of Hillel and Shammai. What is [an example of an argument] not for [the sake of] heaven's name? The argument of Korach and all of his congregation.
For the sake of heaven. That is, to establish truth, or to rebuke people because of their transgression--and not out of a passion to dominate others or to build up a reputation, or to glorify oneself at the expense of others.
Pirkei Aboth, a Commentary by R. Travers Herford, Jewish Institute of Religion, NY, 1945.
Controversy. In the first instance, both sides were serving truth as they saw it; in the other example, Korach's was an unjustified rebellion against authority, and nothing more.
Menachem ben Solomon Me'iri, Provence, 1249-1316, Commentary
Hillel and Shammai. In their debates one of them would render a decision and the other would argue against it, out of a desire to discover the truth, not out of the wish to prevail. That is why, when he was right, the words of the one who disagreed, endured.
Rabbi Ḥiyya bar Abba says: Even a father and his son, or a rabbi and his student, who are engaged in Torah together in one gate become enemies with each other due to the intensity of their studies. But they do not leave there until they love each other, .... at the conclusion of their dispute they are beloved to each other.
-Rabbi Melanie Aron