My guess is that it's just a coincidence. The south side of Chicago is not intrinsically undesirable. There is a lot of open space, there is good public transportation, and there are a lot of beautiful historical buildings. There just happens to be a lot of crime, which pushes the affluent out, who have enough money to not have to deal with that problem. (Of course, there is Chinatown, Bridgeport, and Hyde Park, which are generally fine neighborhoods. The President of the United States lives on the South Side...)