Rav Shneur Kotler explains as follows. Korach’s motivation, although slightly misplaced, came from a good source. That source was the Chazal: קנאת סופרים תרבה חכמה – “scribal jealousy increases wisdom”. We know that competition in Torah study is a motivational force, which expands knowledge.
Korach sought greater closeness with the Ribbono Shel Olam. The problem was that he was a levi and Aharon was a kohen. A kohen does avodah [service] inside the Beis HaMikdosh itself. The leviyim are relegated to a secondary role. Korach's fatal mistake was not recognizing that a kohen is a kohen and a levi is a levi. I.e. each person is born with certain strengths and has a specific role to carry out.
The answer to the question “Why can’t I have a more prominent role?” is that in order to get the job done, different people need to perform different roles. Any person who does his particular role, does it faithfully, and executes it to the best of his ability—the Ribbono Shel Olam is as happy and as satisfied with him as He is with the kohen.