Competing with someone can be the thing that causes a friendship to start. We need to interact with someone to get to know them well enough to become friends. The intensity of competing with one another can be the ideal environment for this.
However, competitiveness can ruin an existing friendship, as any competition has a winner and a loser. Who wants to lose? Who wants to seek out the company of the person they lost to? Who wants to celebrate with the person they lost to?