Equality = Division

The נועם אלימלך notes the Targum on ויקח קרח is ואתפלג instead of the normal Targum of the word, ונסיב.  He connects this with the possuk in Berashis (1:7) ויבדל בין המים אשר מתחת לקריע ובין המים אשר מעל לרקיע where the Targum of ויבדל is also ואתפלג, see there how he explains the connection.  The idea is already from the Zohar (17a.)

Korach's claim was that all men are created equal, כל העדה כולם קדושים, he screamed equality but that call to equality created the greatest divide.  Why does a call for equality create further machlokes and division?  The world is created to have divisions within it.  In fact, the source of division stems from the very creation of the world itself.  The creation of an entity that appears to be separate and devoid of G-d.  It is our job to unite the opposing forces, not to deny their existence.  As an example, the מדות of חסד  and גבורה are opposing forces.  Each one of these מדות has its positives and negatives and they must be deployed in different situations.  One who is a chesed or gevurah only individual will cause serios consequences.  It is the unity of the the two מדות, the middah of תפארת that paints a perfect picture.  The dichotomies in the world are necessary to be able to achieve a perfect balance and unity.  To argue equality without dichotomy leads to the destruction of unity itself.  True equality is to appreciate the talents and lacking in the individuals and to work together to fit everyone's jagged edges into one puzzle; denying the differences and forcing all to be clones only leads to bickering and strife.  This is the message of שני כתובים המכחישים זה את זה עד שיבוא הכתוב השלישי ויכריע ביניהם, it is important to understand the two opposing forces in their own right and only after that to connect them (see Toras Menachem 5751 Nasso.)

The Gemorah Bava Bathra (74a) recounts אמר רבה בר בר חנה: זימנא חדא הוה קאזלינא באורחא [פעם אחת הייתי הולך בדרך], אמר לי ההוא טייעא [ערבי אחד]: תא ואחוי [בוא ואראה] לך את בלועי מחלוקת קרח. אזיל חזא תרי בזעי דהוה קא נפק קיטרא מנייהו [הלך וראה שני בקעים שיוצא עשן מהם]. שקל גבבא דעמרא, אמשייה מיא, ואותביה בריש רומחיה, ואחלפיה התם, איחרך [לקח אותו ערבי גיזת צמר, הרטיבה במים, ושמה בראש רומחו, והעביר אותה שם, ונחרכה] להראותו כמה לוהט המקום.  (brackets is Steinsaltz translation.)  The Maharal notes that there are two holes.  Why two?  He explains that two lines can never form a closed space, you need a third line to complete the triangle.  That is representative of purgatory which is the definition of  a lack of wholesomeness.  That is why Korach's place in purgatory is represented by two holes.  That's why the division of the מים, of the upper waters and the water waters occurs on the second day.

The Gemorah Shabbos (88a) says דרש ההוא גלילאה עליה דרב חסדא בריך רחמנא דיהב אוריאן תליתאי, לעם תליתאי, על ידי תליתאי, ביום תליתאי, בירחא תליתאי.  What is the significance of all the number 3's?
As the Maharal said, The number 3 represents the joining together of two apposing forces.  The giving of the Torah came to heal the greatest divide, that of the world and G-d.  The Torah given to mankind formed a bridge between G-d and the Infinite (see Shemos Rabbah 12:3.)  The number three highlights the point and goal of Mattan Torah and Klal Yisroel.

As discussed in the past, the number 4 (multiple of 2,) represents complete separation.  A box has 4 sides, it is a complete separate entity.  the number 2 is the beginning of the separation and in full form its represented by 4.  Tammuz is the 4^th month (counting from Nissan,) when we are distant from Hashem and that's why the road to churban starts in it.  We must take the lesson of 3 and bring it into the 4, to unite what appears separate with Hashem (see Toras Menachem Korach 5744.)