(יז) 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:
(17) 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.
(ד) בית שמאי מתירין הצרות לאחים, ובית הלל אוסרים. חלצו, בית שמאי פוסלין מן הכהנה, ובית הלל מכשירים. נתיבמו, בית שמאי מכשירים, ובית הלל פוסלין. אף על פי שאלו [אוסרין ואלו מתירין, אלו] פוסלין ואלו מכשירין, לא נמנעו בית שמאי מלשא נשים מבית הלל, ולא בית הלל מבית שמאי. כל הטהרות והטמאות שהיו אלו מטהרין ואלו מטמאין, לא נמנעו עושין טהרות אלו על גבי אלו.
(4) Beit Shammai permit the rivals to the brothers [for marriage], but Beit Hillel forbid [them]. [If these women] had performed Chalitzah Beit Shammai disqualify them from [subsequently marrying] priests, but Beit Hillel allow them [to do so]. [If these women] had undergone Yibum, Beit Shammai permit them [to subsequently marry priests], but Beit Hillel disqualify them [from such a union]. Even though these [one school] prohibit and these [the other school] permit, these disqualify and these allow, Beit Shammai did not refrain from marrying women from Beit Hillel, nor did Beit Hillel [refrain from marrying women] from Beit Shammai. [With regard to] purity and impurity where these ruled [a matter] pure and these ruled [it] impure, they did not refrain from using [utensils] the other deemed pure.
שלש שנים נחלקו ב"ש וב"ה, הללו אומרים "הלכה כמותנו" והללו אומרים "הלכה כמותנו." יצאה בת קול ואמרה "אלו ואלו דברי אלהים חיים הן, והלכה כב"ה." וכי מאחר שאלו ואלו דברי אלהים חיים, מפני מה זכו ב"ה לקבוע הלכה כמותן? מפני שנוחין ועלובין היו ושונין דבריהן ודברי ב"ש. ולא עוד אלא שמקדימין דברי ב"ש לדבריהן
For three years, the House of Hillel and the House of Shammai argued. One said, 'The halakha (law) is according to our position,' and the other said, 'The halakha is according to our position.' A heavenly voice spoke: "These and those are the words of the living God, and the halakha is according to the House of Hillel." A question was raised: Since the heavenly voice declared: "Both these and those are the words of the Living God," why was the halacha established to follow the opinion of Hillel? It is because the students of Hillel were kind and gracious. They taught their own ideas as well as the ideas from the students of Shammai. Furthermore, they even taught Shammai's opinions first.
Mikdash Melech to Zohar Parshat Bereishirt 17b
In the time of the Messiah, we will follow the law according to Shammai. Hillel represents kindness and Shammai severity (hence the rulings of Beit Hillel are almost always more lenient). When the Messiah comes the advantage of the severity will be revealed and therefore the law will be in accordance with Beit Shammai. Beit Shammai comes from such a high level this present world is incapable of withstanding it, and only when the Messiah comes will we be able to follow their opinion.
שוב מעשה בנכרי אחד שבא לפני שמאי א"ל גיירני ע"מ שתלמדני כל התורה כולה כשאני עומד על רגל אחת דחפו באמת הבנין שבידו בא לפני הלל גייריה אמר לו דעלך סני לחברך לא תעביד זו היא כל התורה כולה ואידך פירושה הוא זיל גמור.
Another time a non-Jew came before Shammai and said, "I will convert if you can teach me the entire Torah while I stand on one foot." Shammai pushed the non-Jews aside with the ruler that was in his hand. The non-Jew came before Hillel and Hillel converted him saying, "What is hateful to you, do not do to your neighbor, that is the entire Torah, the rest is just commentary, now go and study."
Rabbi Nachman of Bratzlav, Likkutei Etzot, Shalom, #10
The essence of shalom is to unite two opposites. Therefore, do not be alarmed when you meet someone whose opinions are diametrically opposed to yours, causing you to believe that it is absolutely impossible to live with him in peace. Similarly, when you see two people of extremely contrasting natures, do not say that it is impossible to make peace between them. On the contrary, the very essence of peace is to strive for harmony between opposites, just as God makes peace in the heavens between the contrasting elements of fire and water.
מקום בו אנו צודקים
יהודה עמיחי
מִן הַמָקוֹם שֶׁבּוֹ אֲנוּ צוֹדְקִים
לֹא יִצְמֵחוּ לְעוֹלָם
פְּרָחִים בָּאַבִיב.
הַמָקוֹם שֶׁבּוֹ אֲנוּ צוֹדְקִים
הוּא רַמוּס וְקָשֶׁה
כְּמוֹ חֲצֵר.
אַבָל סְפֵקוֹת וְאֲהָבוֹת עוֹשִׂים
אֵת הַעוֹלָם לְתַחוּחַ
כְּמוֹ חַפָרְפֶרֶת, כְּמוֹ חַרִישׁ.
וּלְחִישָׁה תִּשָׁמַע בַּמָקוֹם
שֶׁבּוֹ הָיָה הַבָּיִת
אֲשֶׁר נֵּחֵרַב.
The Place Where We Are Right
by Yehuda Amichai
From the place where we are right
Flowers will never grow
In the spring.
The place where we are right
Is hard and trampled
Like a yard.
But doubts and loves
Dig up the world
Like a mole, a plow.
And a whisper will be heard in the place
Where the ruined
House once stood.