Not admitting my mistakes came from a sense of superiority and pride. I thought I'm the leader so I must be right. I now understand leadership differently. It's a servant role (or as Robert Greenleaf puts it - servant-leadership).
And like anyone in organizations or committees, you are never going to have all of the answers. Revealing you are human is helpful; good leaders go and find the answers the team needs. But first, if he or she don't know, admit it... Then find the answers ☺
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THINK BIG. START SMALL. GO DEEP.