Why do some fellowships require "leadership experience"?

The fellowship I'm about to apply requires me to express my past leadership experience in the personal statement. Why? I understand that leadership is a soft skill that everyone should have, but this is academia, not business. People in this environment put cooperating before leading. Of course, even in business, there is no group that work like in military, the person in low level still can suggest idea and change the leader/manager's mind. The role of the leader is inspire and amalgamate separate people to one united unit. But in academia, everyone should inspire themselves, and the science itself are the glue to attach people together, right? So why don't these fellowships require me to show my past cooperation, rather than leadership?