During the course of career mode you probably be given a rematch (I say probably because you don't pick your opponents and I've done entire careers never getting a rematch.) In order to get a rivalry fight you have to LOSE any non-title rematch. The next fight should be a rivalry fight against the fighter you just lost to.
NOTE: This must be done before attaining a title. Losing a rematch for a title will NOT get you a rivalry fight. You have three leagues to do this in, so if you still dont have it after you win the Strikeforce or Mystic belt than you can just lose a couple fights to rank down then start winning again and hope you get a rematch. The career mode is always 40 fights long.