Notre Dame beat Michigan in 1909 and they were scheduled for another game in 1910, but before the game Michigan coach Fielding H. Yost protested Notre Dame's intended use of two players that he believed were ineligible. Notre Dame refused to bench the players and so Michigan canceled the game and Yost refused any further games with Notre Dame. Yost went so far as to influence the other schools in the then-Western Conference (predecessor to the Big Ten), to refuse to admit Notre Dame to the conference or to schedule games with them (there was a lot of anti-Catholic language used). Because the Western Conference largely would not schedule them, the Irish scheduled games against schools on the east and west coast, which is how our USC rivalry began. It helped the Irish become a national program.
Now, if the Big 10 wants us, I say too bad.