Rashi says that Korach "took himself." He revealed the essence of his being, his soul. Rashi further states that "he took himself to one side." Rashi says he did this to "separate himself from the congregation." His wish was to elevate himself above everyone else. He wanted to be uplifted in the same manner as a Kohen Gadol. Rashi quotes the Aramaic word used by Targum Onkelus: "he separated himself." His entire desire was to rise above the rest of the nation by reaching the level of a High Priest. He wanted to be "... separated ... to be most holy."
Korach went even further, saying that "the entire congregation is all holy." Rashi comments, "...All of them heard Hashem's words at Sinai from His mouth (as to speak) ... Not only did he hear at Sinai, 'I am the Lord, your G-d,' the entire congregation heard it." He claimed that we all received the Torah together from Hashem. At that time, all Jews became "a nation of Kohanim." As explained by the commentaries, we all became fit to become High Priests. This was Korach's claim when seen through the prism of the "wine of Torah."
(Adapted from a talk given on Shabbos Parshas Korach, 3 Tammuz 5748)