Competition is a healthy motivator for high achievement, performance, and growth. We experience competition when being surrounded by peers and colleagues with similar tasks and goals that challenge us, whether athletically, artistically, academically, professionally, or otherwise. This process usually sharpens our drive and ability to succeed as individuals and as a community.
Rivalry is competition taken to an unhealthy extreme. It is "othering" the competition, diminishing the humanity of opponents instead of learning from them. We see this happen with violent sports fans, cutthroat artists, mudslinging politics, and consumerism. This process tears our broad and local communities apart, destroys empathy and communication, and puts all of us in a foul mood.