Korah and his co-conspirators rebelled against Moses and Aaron, claiming that they were perverting religious authority and arrogating authority to themselves. “We know better” he and his co-conspirators said, “we are the rightful authority not you.” Indeed, they use words similar to those used by Moses himself several chapters earlier, when he said in response to Joshua “Don’t worry about my position. If only everyone was a prophet and the spirit of God was upon them.” And Miriam and Aaron both say “God has spoken to us too.” Korah says “All the people are holy and God rests upon them.” Who can argue with that? Korah was elevated as a Levite. But this clearly was not enough. He wanted more. Not only but allowed a lot of other disaffected Israelites to rally around him regardless of the legitimacy of their claims.
But if they had the right to challenge, and if their main argument simply echoed the words of Moses, why then do we regard them as rebels who deserved punishment? In my opinion it is not whether their claim to holiness was right or not. But because they used negative, abusive language and arguments falsely, to support their claims. They were dishonest. Moses replies “Why are you complaining about me? I have not abused power or taken anything for myself.” He realized the holiness argument was just a cover for personal gain.
The Midrash says that Korah tried to claim religious authority, that he was more religious than Moses and understood Torah better. In fact, he was challenging the Divine authority. HaShem intervened on Moses’s behalf. But they were belittling him personally. And this has always been our Achilles heel. People, even very religious ones, often think that belittling wins an argument. It doesn’t. It simply reflects badly on those you use it as a tool for their own ends.
Just like Korah they will not succeed not matter what titles they have, because Hashem considers a person’s heart and pays no attention to abusive words.