“Moshe said to Korach, "Please listen, sons of Levi. Is it not sufficient for you that the G-d of Israel has elevated you over the rest of the congregation of Israel to bring you closer to Him to perform the services of the Mishkan (Tabernacle) of Hashem, and to stand before the congregation to minister to them? And He brought you near with all of your brethren the sons of Levi with you - and yet you demand to be kohanim (priests) as well? 16:8-10
It is important to recognize that Korach’s rebellion attacked more than just Moshe’s choice of Aaron, his brother, as high priest. Accusing Moshe of nepotism was an attack on Moshe’s personal integrity, and would undermine everything Moshe had done as a leader, most importantly the giving over of the Torah. The charge was totally baseless: Korach ignored the fact that for all Moshe’s sacrifices on behalf of the people, he himself would merit neither the priesthood nor the monarchy. None of his children would ascend to positions of prominence. As a leader, his service of the Jewish people was a model of perfect altruism. Yet, members of his own tribe ignored this completely, and accused him of nepotism! This baseless charge, if left uncontested, would poison the national attitude toward Moshe, and eventually destabilize the entire infrastructure that he had built. This left Hashem with no option other than to remove Korach and his followers from the nation, lest they pollute the national attitude even further.