Texas football has played, but never beaten these FBS teams
Texas football vs. Mountain West
Texas has largely dominated competition from the Mountain West. The Longhorns hold an all-time record against the current Mountain West schools of 14-1-0. That sole loss against the Mountain West just happened to come in the only time Texas faced the Air Force Falcons.
Otherwise, Texas is undefeated in multiple tries against the Wyoming Cowboys, Utah State Aggies, and New Mexico Lobos. Texas is also undefeated in one try each against the San Jose State Spartans, Hawaii Rainbow Warriors, and Colorado State Rams.
Texas has yet to face some bigger programs in the current Mountain West, such as the Boise State Broncos and San Diego State Aztecs.
Air Force (0-1-0)
As with losses to Minnesota in 1936 and Syracuse in 1960, Texas had a weird and unlikely culmination of circumstances come together in 1985 when it faced Air Force in the non-conference portion of the regular season schedule.
Texas faced the best team in Air Force program history (according to the Simple Rating System) in the 1985 Bluebonnet Bowl. This Air Force team was one single-digit loss to the defending National Champion BYU Cougars away from being able to compete for a national title in 1985.
Air Force clearly had a chip on its shoulder heading into the 1985 Bluebonnet Bowl against the Longhorns. Two costly interceptions caused Texas to fall short of Air Force in the 1985 Bluebonnet Bowl, 24-16.