Now rivalries can be taken to extremes sometimes, most are friendly rivalries, but KU's rivalry with Missouri actually has some significant historical context to it. And realize it or not, that history between the 2 states played a major role in the start of the civil war back in the 1860's.
This is a photo of a painting hanging at the state capitol in Topeka. It is John Brown, a noted abolitionist, depicted as a warrior for the cause of freedom.
Kansas became a state in January of 1861, the civil war commenced about 3 months later. But for Kansas, the battle over the legality of slavery commenced about 8 years earlier and was largely a battle with, you guessed it, Missouri.
Missouri was a "slave state" and many Missourians wanted Kansas to be a "slave state" also. Many new settlers moved into Kansas from various parts of the country during the 1850's. In Kansas, the population was split (pro or anti slavery) and there was actually 2 cities vying to become the state capitol, one pro-slavery, the other anti-slavery. Lawrence, where KU is located, was an important community for so-called free-staters (anti slavery).
Kansas was eventually admitted to the union as a free state, but the process was not easy and at times became very bloody.
Here's a link for a brief discussion of those days.
Bleeding Kansas link: http://en.wikipedia.org/wiki/Bleeding_Kansas
Two very colorful people were part of this history. One was John Brown.
And here is a link for information on him.
John brown link:
The other was William Quantrill, a pro slavery advocate. And here is a link for more information.
William Quantrill Link