I think not because it makes people more competitive. It can also create rivalry and enmity between the athletes. Moreover, the supporters of one team will also be in a conflict with the supporters of the other team. Its because everyone wants their country to win every event in which they participate. This separates us and its out nature so it can't be helped.
Incorrect, football brings along celebrations like the super bowl party. The common sport brings thousands--even millions of fans into the same arena and though people become more competitive it shows an unspeakable chemistry link between the two. You cannot say that sports tears us apart. If anything, it helps us find who we can easily debate sports with. State your next argument.
The major games for any sport that take place once a year bring fans together for food and a rush of hormones, watching a bunch of intense sports players compete for some of the most valued championships in sports entertainment history. How does this not bring fans together for at least one day a year? Also, friends can tend to meet up even in basic events (like WWE's Raw or Smackdown). Thousands of fans just watching their most valued sports...together. Yes arguments start, but it's natural.