Why did Rabbi Yochanan Ben Zakkai point out the dominant traits of his students?

Isn't that a source of unnesaary competion between the students?

Rabbi Jeff Wohlgelernter discusses this and more in PART 2 of this mishna.

Perek 2 Mishna 8 PART 2-

רַבָּן יוֹחָנָן בֶּן זַכַּאי קִבֵּל מֵהִלֵּל וּמִשַּׁמָּאי. הוּא הָיָה אוֹמֵר, אִם לָמַדְתָּ תוֹרָה הַרְבֵּה, אַל תַּחֲזִיק טוֹבָה לְעַצְמְךָ, כִּי לְכָךְ נוֹצָרְתָּ. חֲמִשָּׁה תַלְמִידִים הָיוּ לוֹ לְרַבָּן יוֹחָנָן בֶּן זַכַּאי, וְאֵלּוּ הֵן, רַבִּי אֱלִיעֶזֶר בֶּן הוֹרְקְנוֹס, וְרַבִּי יְהוֹשֻׁעַ בֶּן חֲנַנְיָה, וְרַבִּי יוֹסֵי הַכֹּהֵן, וְרַבִּי שִׁמְעוֹן בֶּן נְתַנְאֵל, וְרַבִּי אֶלְעָזָר בֶּן עֲרָךְ. הוּא הָיָה מוֹנֶה שִׁבְחָן. רַבִּי אֱלִיעֶזֶר בֶּן הוֹרְקְנוֹס, בּוֹר סוּד שֶׁאֵינוֹ מְאַבֵּד טִפָּה. רַבִּי יְהוֹשֻׁעַ בֶּן חֲנַנְיָה, אַשְׁרֵי יוֹלַדְתּוֹ. רַבִּי יוֹסֵי הַכֹּהֵן, חָסִיד. רַבִּי שִׁמְעוֹן בֶּן נְתַנְאֵל, יְרֵא חֵטְא. וְרַבִּי אֶלְעָזָר בֶּן עֲרָךְ, מַעְיָן הַמִּתְגַּבֵּר. הוּא הָיָה אוֹמֵר, אִם יִהְיוּ כָל חַכְמֵי יִשְׂרָאֵל בְּכַף מֹאזְנַיִם, וֶאֱלִיעֶזֶר בֶּן הוֹרְקְנוֹס בְּכַף שְׁנִיָּה, מַכְרִיעַ אֶת כֻּלָּם. אַבָּא שָׁאוּל אוֹמֵר מִשְּׁמוֹ, אִם יִהְיוּ כָל חַכְמֵי יִשְׂרָאֵל בְּכַף מֹאזְנַיִם וְרַבִּי אֱלִיעֶזֶר בֶּן הוֹרְקְנוֹס אַף עִמָּהֶם, וְרַבִּי אֶלְעָזָר בֶּן עֲרָךְ בְּכַף שְׁנִיָּה, מַכְרִיעַ אֶת כֻּלָּם:

Rabban Yohanan ben Zakkai received [the oral tradition] from Hillel and Shammai.He used to say: if you have learned much Torah, do not claim credit for yourself, because for such a purpose were you created. Rabban Yohanan ben Zakkai had five disciples and they were these: Rabbi Eliezer ben Hyrcanus, Rabbi Joshua ben Hananiah, Rabbi Yose, the priest, Rabbi Shimon ben Nethaneel and Rabbi Eleazar ben Arach. He [Rabbi Johanan] used to list their outstanding virtues: Rabbi Eliezer ben Hyrcanus is a plastered cistern which loses not a drop; Rabbi Joshua ben Hananiah happy is the woman that gave birth to him; Rabbi Yose, the priest, is a pious man; Rabbi Simeon ben Nethaneel is one that fears sin, And Rabbi Eleazar ben Arach is like a spring that [ever] gathers force. He [Rabbi Yohanan] used to say: if all the sages of Israel were on one scale of the balance and Rabbi Eliezer ben Hyrcanus on the other scale, he would outweigh them all. Abba Shaul said in his name: if all the sages of Israel were on one scale of the balance, and Rabbi Eliezer ben Hyrcanus also with them, and Rabbi Eleazar ben Arach on the other scale, he would outweigh them all.

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