This paragraph sums up Baylor best:
Between 1925 and 1995, Baylor played Rice, SMU and TCU every single season with two exceptions — during a time of war in 1943-44, and again in 1987-88 when the Mustangs did not field a team due to NCAA sanctions. Since 1995, Baylor has played Rice and SMU just twice and TCU three times. Why? BU was part of the SWC membership that bolted for the Big 12 after that conference officially launched in 1996. For some reason, those historic rivalries were willingly allowed to fall by the wayside by Baylor 16 years ago.
Also just to clarify because people seem to get this wrong, Baylor University != Baylor College of Medicine. BCM is a completely separate institution as of 1969. Baylor is no where near as academically remarkable as people seem to give them credit.