The Gemara in Sanhedrin (110A) learns from the passuk “and you shall not be like Korach and his assembly” that it is prohibited to engage in machlokes. The Zera Shimshon asks, why by this aveirah do we mention his name, why don’t we say don’t make machlokes or the like. By no other averia does it say this “don’t kill like so and so” or the like.
Says the Zera Shimshon that the Torah is conveying to us the gravity of the sin of machlokes, whether he is being attacked and only retaliating or initiating the attack. The Zera Shimshon explains that when we inflict pain on another and disgrace him, then the Shechina has pain. For every person is a tzelem elokim, so in essence, he is disgracing the Shechinah which is in his fellow man as well.
So too Korach should have realized that even if Moshe had chosen Aaron, Hashem did not rebuke him. On the contrary, Hashem rested His Shechina in the Mishkan. If so, he was arguing with the Shechina itself, and so too anyone who engages in machlokes is considered like he is disgracing the Shechina.