If I'm the Yankees, I want to avoid this series going to seven games at all costs. If the Angels take game six, they are going to have so much going for them that I'm not even sure how much of an advantage it would be to have CC on the mound for game seven. Obviously I would rather have him over anyone else, but I think it's extremely important for the Yankees to avoid a game seven.
Also, with the way Hughes and Joba have looked, it might be important to have CC available for both games (one as a starter, and one to pitch to at least a couple batters late). The only way you can do that is if he starts game six.