I'm a huge Cubs fan.  The only thing that would trump the Cubs would be the Bears.  One thing I never understood as a Cubs fan though, is the animosity between Cubs and White Sox.

RIVALRY
Other than the two series that they play each year, there is no good reason for the hatred between the two fan bases.  Chicago is lucky enough to have two very active ball clubs that represent the area.  We should embrace it, not ruin it with senseless banter.  They are not even in the same league let alone the same conference.  But, there is that primal thought that fuels the fire:  "My team is better than yours!"  

SOLUTION
As I said earlier, both fan bases should embrace the privilege of having two major league ball clubs.  It's rare that they are both in the post season, so when one goes down, the two fan bases should consider supporting the other.  In theory, this would create a bigger buzz among the baseball community to potentially attract future talent to the city.  Also, if a person is a true baseball fan, they should appreciate the other teams success because that means you are able to watch good quality baseball for a longer period of time than you would if there was only one local team that is readily accessible.  Just embrace the fact for that season, your team just didn't cut it.

To conclude, I will leave you with a quote from the famous philosopher Rodney King, "Can't we just all get along!"  

P.S.  Now if you're talking about the St. Louis Cardinals..that's a different story.  The only other team that would be worse to support than them, would be rooting for the Packers.  Now that is just inexcusable!