Rashi explains that there were many ideological strands to Korach’s rebellion against Moses’s leadership. One was a cry of egalitarianism - “All the congregation are entirely holy (Rashi: all heard directly from God at Mount Sinai) and why do you make yourself ruler over the assembly”.
Yet other causes of Korach’s dissent were far less populist. He was affronted by his exclusion from the hierarchy that Moses had appointed over the Levites, claiming that he had a better claim to the princeship of the sub-tribe than his cousin who had been given the role; he believed that the Levites should have the same roles as the Cohanim in the Tabernacle; and he was joined by Reubinites, seeking to restore their rights as the firstborn tribe.
Then, as now, rebels galvanise the masses with their calls for equality, which actually cloak their desires for something very different - power for themselves.