Rivalries are born through battles for supremacy. Epic matches with championship implications mold the disdain for an opposing team. Run into this team on multiple occasions, and boom. You have your rivalry.
They typically don’t occur between opponents who face each other just once. You can’t tell me that the Suns and Bulls are rivals simply because they faced off in the 1993 NBA Finals.
No, rivalries take time, with team and/or players developing an animosity for one another. Story lines develop, fan bases begin to turn on one another, and the jokes begin.