It teaches students the real lessons of the world and it prepares us for events like unexpected loss and learning how to win professionally and not boastfully, and it's good to learn these things before going off to the adult world and becoming a working citizen in this society. If there were no competition in schools, most of the life lessons that many of us have acquired today would probably be oblivious to us before we become adults.
Competition in schools, if not taken to an extreme, is a good thing as it prepares children for the ultra-competitive job market. Doing your best and learning from losses is a way to deal with successes and failures related to work and making money. We live in a consumer-based society where sales and moneymaking is a way of life. In order to cope, children should learn how to compete early in life and in a school setting whether through athletics or academics or both.
Competition creates two sides.... Winner and Loser. These sides are completely relative to what the competition is. You may be on the losing side here, and the winning side over there...
Losers: (assuming you discourage bullying...) the Loser learns the basics of life... Trying harder and not only succeeding. You will never know how to fail if you have never been allowed to fail, and learning how to fail is important, beyond all things.
Winners: It'll teach sportsmanship, and the need to compete. It really doesn't have as many benefits as Losing does... The best one though is building confidence. With enough competition, everyone can be in the winning bracket (or in the higher ranks) inspires people. It gives them confidence and faith in themselves.
Just make sure everyone has a chance to win at least a few times, and keep it fair.