http://en.wikipedia.org/wiki/Notre_Dame_Fighting_Irish_football_rivalriesMiami is listed as a past rival, but they haven't played since 1990.
You, as a player, may have seen Miami and Michigan as your top rivals, but fans of college football don't get to be in the locker room. Perception to most fans throughout the nation is USC, Michigan, Michigan State, Purdue, and more recently Boston College (which may be ending).
Plus, I don't know about in the locker room, but to Michigan fans its losing to Ohio State that can get a coach fired. Not losing to Notre Dame.
ND vs. USC 42-32-5 (79 games) played every year except during WW2
ND vs. Michigan State 42-27-1 (70 games)
ND vs. Purdue 52-26-2 (80 games)
ND vs. Michigan 20-15-1 (36 games) renewed in 1978
ND vs. Boston College 9-9 (18 games) tied series
ND vs. Miami 15-7-1 (23 games) ended in 1990
Can you understand why someone might feel that USC, Michigan State, Purdue, and Boston College are a bigger rivalry than Miami who hasn't played ND since 1990. Plus, I don't deny that Michigan is a big game for ND. But historically, USC is the bigger game. Plus, recently the BC game has been huge (though like I said it looks like it may be ending, series tied 9-9).