They don't. But the player who holds it should be a leader themselves otherwise it makes a mockery of the concept of team leader.
I can't think of a reason Jagielka should be our captain. He doesn't organise his back four, he doesn't act to confront referees on behalf of the team, he obviously feels uncomfortable representing the club in post match interviews.
He's the captain Moyes made just before leaving for United and he's saddled us with one of our worst in my memory.
Oh David.