Korach split from the root by grabbing gifts

ופירוש ויקח תרגום ואתפלג.

And the meaning of "Vayikach" (And Korach took) (Bamidbar 16:1) — the Targum renders it "v'isp'lag" (and he separated himself).

The Sefas Emes opens by noting that Onkelos translates "and Korach took" as "and he split off," indicating that Korach's "taking" was in truth an act of separating himself from the community and its root.

ועוד אמרו שלקח מקח רע לעצמו.

And further, [Chazal] said that he took a bad acquisition for himself.

Chazal also explain "vayikach" to mean that Korach made a bad bargain for himself — he "took" something to his own detriment.

דאיתא במד' מטות ג' מתנות בעולם זכה בא' מהן זכה בכל חכמה גבורה עושר אימתי בזמן שהן מתנות שמים ובאין בכח התורה ע"ש.

For it is brought in the Midrash (parshas Matos): there are three gifts in the world — one who merits one of them has merited all: chochmah (wisdom), gevurah (strength), and osher (wealth). When? When they are gifts of Heaven and come through the power of the Torah — see there.

The Midrash teaches that wisdom, strength, and wealth are precious only when they are received as gifts from Heaven, channeled through the Torah and subordinated to it. Only then does possessing one amount to possessing all.

לכן הי' צריך קרח לבטל חכמה ועושר שלו אל התורה דכתיב אורך ימים בימינה בשמאלה עושר וכבוד.

Therefore Korach needed to nullify his wisdom and his wealth to the Torah, as it is written, "Length of days is in its right hand; in its left hand, wealth and honor" (Mishlei 3:16).

Korach was both wise and immensely wealthy. His task was to surrender these gifts in bittul (self-nullification) to the Torah — for the verse teaches that wealth and honor flow from the Torah ("in its left hand"), not as independent possessions.

אבל הוא לקח לעצמו ואתפליג מן השורש כמ"ש שם המדרש חוטפין לעצמן ולכן לא הי' לו קיום.

But he took for himself and split off from the root, as that Midrash says, "they snatch for themselves," and therefore he had no endurance.

Instead of nullifying his gifts to the Torah, Korach grabbed them as his own — "snatching for themselves" — and thereby severed himself from the root that gives life. Cut off from the source, his standing could not endure, and he was swallowed by the earth.

ואהרן היו כל מעשיו דבוקין בשורש ועליו נאמר ותקעתיו יתד במקום נאמן ומתקיים לעד.

But Aharon — all his deeds were cleaving to the root, and of him it is said, "I will fix him as a peg in a firm place" (Yeshayahu 22:23), enduring forever.

Aharon's opposite path: every act of his stayed bound to its supernal root, so he was like a peg driven into solid ground. What is rooted in the source endures eternally, which is why Aharon's staff and priesthood lasted.

וזה נק' אורך ימים כח השורש כי כח הכהן הוא מן השמים כדאיתא בגמ' כהני שלוחי דרחמנא דמי איכא מידי דאנן לא מצינן למיעבד ושליח מצי כו'.

And this is called "length of days" — the power of the root; for the power of the Kohen is from Heaven, as it is brought in the Gemara: "the Kohanim are like emissaries of the Merciful One — is there anything that we ourselves cannot do, yet an agent can?" (Kiddushin 23b).

"Length of days" denotes the enduring power of the root. The Kohen's power is heavenly: the Gemara debates whether Kohanim are our agents or Heaven's, raising the principle that an agent can only do what the one who sends him could do himself — which forces the conclusion that the Kohen acts as Hashem's agent, drawing his power from above.

ואמת כי שניהם אמת שבנ"י נותנים כחן להכהן ונעשה בזה כלי לקבל כח עליון.

And in truth both are true: that Bnei Yisrael give their power to the Kohen, and thereby he becomes a vessel to receive supernal power.

The Sefas Emes harmonizes the two views: Bnei Yisrael do invest the Kohen with their power, but this very investment makes him into a vessel that then receives a higher, Heavenly power. He is simultaneously the people's agent and Hashem's.

וקרח סבר כהני שלוחי דידן בלבד לכן נדמה לו כי בודאי גם אנן מצינן למיעבד כדאמר כולם קדושים אבל באמת כח הכהן בעזר עליון והוא שלוחא דרחמנא וזהו הי' האות מטהו יפרח [שוב ראיתי במד' עצמו פ' מטות דורשו על קרח]:

And Korach held that the Kohanim are our agents alone; therefore it seemed to him that surely "we too can do it," as he said, "all of them are holy" (Bamidbar 16:3). But in truth the Kohen's power is by supernal help, and he is the emissary of the Merciful One; and this was the sign, "his staff shall blossom" (Bamidbar 17:23). [I later saw in the Midrash itself, parshas Matos, that they expound it concerning Korach.]

Korach's error was holding that the Kohanim are merely the people's agents — so he reasoned that since "all the congregation are holy," anyone could serve. But because the Kohen in fact acts by Heavenly power, this could only be proven by a sign no human power could produce: the dry staff of Aharon blossoming. The blossoming demonstrated that the Kehunah is rooted above, not in human appointment. The Sefas Emes adds that he afterward found the very Midrash (Matos) applying this idea to Korach.

Summary: Reading "vayikach" through the Targum ("he split off") and Chazal ("a bad acquisition"), the Sefas Emes explains Korach's downfall: the three gifts of wisdom, strength, and wealth endure only when nullified to the Torah and received as Heaven's gifts. Aharon kept all his deeds cleaving to the root, so he endured "like a peg in a firm place"; the Kohen's power is ultimately Hashem's, even as Bnei Yisrael make him a vessel for it. Korach, holding the Kehunah to be merely the people's appointment, "snatched for himself" and split from the root — and the blossoming of Aharon's staff was the sign that the Kehunah's power comes from above.