I think the catalyst was really independents started to join conferences. Between 1990 and 1992, Boston College, Rutgers, Syracuse, West Virginia, and Virginia Tech all joined the Big East. The ACC added Miami and Pitt in 1991. The SEC added South Carolina (and grabbed Arkansas from the SWC) in 1992. The B10 added Penn St in 1993.
That left the Big 8 as "small" conference, and the SWC as both small and geographically limited (Arkansas had been the only member outside of Texas), to say nothing of their, ahem, colorful history. The obvious solution was for Texas, ATM, TT and TCU Baylor to join up with the Big 8 and be on par with the other conferences.
Round 2 was kicked off by the B10 building their own network (after the B12 passed because Texa$ wanted one for themselves, or with just ATM and maybe OU), and saw in influx of cash. Then Nebraska got mad that one program (Texas) was getting more money than than the other three programs (NE, ATM, OU) that were supposed to get more money than everyone else (the other 8 B12 members). Never mind who insisted on unequal revenue distributions to start with.