Okay so you fired someone, then decided later to bring them back. This means whatever guideline you use to fire people is floppy or petulant, you caved to public backlash, or the firing guidelines are clear but the information you took grave actions upon was bad (was unreliable and/or unverified).
Anyway, none of those things are good markers of leadership.
Edit: Forgot another reason for recanting a firing: your boss told you that you don’t have the authority. Nothing takes away your leadership teeth like that…