Two biggest responsibilities of a team captain:
1. Keep teammates focused and organized when they become distracted or demoralized (e.g. bad call from the ref., bad foul, heads dropping when down 2-0, having an argument with someone else on the pitch. etc.)
2. Be the team representative when interacting with the referee when things boil over.
Both of these roles are about attitude and interpersonal skills. They have little to do with speed, positioning, and ball skills, even though those attributes are essential to being selected to be on the pitch. Gaz attributes to be a good captain are are probably obvious to the rest of the team and the coaching staff based on their interactions with him and the way they have observed him interacting with refs., but hard for fans to see. Being captain is not the same as being the most popular player to the fans.
Carey is probably our most creative player and probably the most popular, but he gets very emotional about calls and gets in the face of referees. That is fine, but not what you want your captain doing. At times, Gaz will likely be talking the ref out of giving Carey a card and earning his captain's armband that way.