The Parsha begins with Korach gathering an assembly to rise up against Moshe and Aharon, and tells us as follows.
ם רַ ב לָכֶם כִּי אֲלֵהֹאמְרוּ רֹן וַיֲה וְעַל אַהֲ עַל מֹשּלוֲּ ָהִקּוַי עַלּׂ ְאוִּתְנַשּעַ תּוּמַדּכָם ה' וֹבְתוִּים וּשׁשָֹם קְדּעֵדָ ה כֻּלָכָל ה : (טז ג)ל ה'ַקְה- They gathered together against Moshe and against Aharon and said to them, “It is much for you! For the entire assembly, all of them, are holy and Hashem is among them, so why do you exalt yourselves over the congregation of Hashem?”
After the ground opened up and swallowed Korach and his family, and the fire broke out and burned Korach’s assembly, the Jews complained to Moshe and Aharon telling them that it was them who caused Korach and his people to die. As a punishment for that, a plague broke out and killed many Jews. Following the Jews’ complaints and the subsequent plague, Hashem wanted to demonstrate to the Jews that it wasn’t Moshe and Aharon who chose themselves, rather it was He, Hashem, who chose them, and He thus commanded Moshe to do as follows.
דבר אל בני ישראל וקח מאתם מטה מטה לבית אב וכו' איש את שמו תכתב על מטהו. ושם אהרן תכתב על מטה לוי וכו' והיה האיש אשר אבחר בו מטהו יפרח והשכתי את תלנות בני ישראל אשר הם מלינים עליכם. וכו' והנה פרח מטה אהרן לבית לוי ויצא פרח ויצץ (י"ז יז-כג)ציץ ויגמל שקדים. - Speak to the Children of Israel and take from them one staff for each father’s house... each man’s name shall you inscribe on his staff. And the name of Aharon you shall inscribe on the staff of Levi... It shall be that the man whom I shall choose, his staff will blossom; and I shall thus subside from upon Me the complaints of the Children of Israel, which they complain against you... And behold! The staff of Aharon of the tribe of Levi had blossomed; it brought forth a blossom, sprouted a bud and developed almonds.
The Sefer זרע ברך quotes a Midrash that says that the blossoms were inferring to Hashem’s choosing of the children of Aharon, while the buds which sprouted were inferring to Hashem’s choosing of Aharon himself. This would seem superfluous, for we don’t find Korach’s arguments directed towards Aharon’s children but rather towards Aharon himself, and therefore confirming Aharon’s status would have been sufficient. Furthermore, even if we were to understand Korach’s arguments to be directed towards Aharon’s children as well, nevertheless it still would seem out of place to confirm the status of Aharon’s children even before confirming the status of Aharon himself, being that all that Korach clearly stated in his argument was Aharon himself.
We can explain that there was an inherent difference between what Korach saw as ‘Moshe taking the royalty for himself’, and what he saw as ‘Moshe taking the Kehunah for his brother Aharon’. For in regards to royalty, the only Jewish lineage of royalty is that of the tribe of Yehuda. Royalty of any other tribe isn’t a lineage, and thus its kingship would only be passed down to the king’s son if he is fit and worthy to rule, otherwise the kingship would go to another who is indeed worthy of it. Therefore, when Moshe ‘took the royalty for himself’, it wasn’t a lineage of royalty that he took, rather he merely took royalty for himself alone, for his son would need to earn the kingship anew if he would want to rule after his father. Yet in regards to Kehunah it isn’t so, for Kehunah definitely is a lineage and a consequential inheritance, whereas each Kohen doesn’t need to take the Kehunah anew, rather if his father is a kohen he will naturally be a kohen as well. Therefore, when Moshe chose the priesthood for Aharon, it wasn’t Aharon alone to whom he gave the Kehunah, rather he was essentially giving it to all the coming generations of Aharon, as well.
Accordingly, we can explain that It wasn’t so much that Korach was envious of the royalty and priesthood that Moshe took for himself and for his brother Aharon. What really caught his envy was the lineage of priesthood that Moshe gave to Aharon; that was something that made Korach very jealous and resentful. Thus, although indeed Korach never specifically mentioned Aharon’s children, nevertheless it was predominantly Aharon’s children’s getting the Kehunah that Korach complained about, and which caused him to do what he ultimately did. Consequently, when Hashem wanted to defuse Korach’s arguments, He specifically inferred to Aharon’s children being chosen for the Kehunah, even before inferring to Aharon’s own Kehunah, for it was indeed Aharon’s children which Korach was primarily upset about.
זרע שמשון פרשתנו אות ב