The Chicago White Sox are a young bunch. They have lots of players that are young and are still finding their way in the big leagues. Although Jose has never made it to the postseason before in his career, he still knows what it is like to be a professional in big moments. He has proven time and time again that he can be a big-time player in big-time moments. There are lots of young players that need that sort of leadership around.
All winning Major League teams have a guy like Abreu on their team. Everyone needs a guy that can take control of a clubhouse and lead the way. Abreu has basically been the face of the White Sox since he arrived on the scene and is respected as such. There is also a sense of leadership that is put on players who are good. Sometimes your skills on the field land you into the role of a leader both on and off the field.
Abreu would likely be the de facto captain of the team if he were to come back. They don’t really have that many veteran players pre-free agency. Abreu is absolutely capable of doing that for this team as they start to try and be a really good baseball team.