Most friends can have a healthy comeptitive friendship. Its cool to play xbox and see who is going to win, and that lasts for a good while until its only one kid who wins time and time again.
So, here's the deal. When friends (like Gene and Finny) have one who has a power over the other, competition becomes dangerous. Finny is really cool and Gene is impressed. Gene admires Finny to a point that makes us wonder as readers. Gene wants to impress Finny and makes a point to show his ability in academics to outweigh or one-up Finny's athletic ability. The problem with this surfaced when Gene pushes Finny out of the tree probably unintentionally but intentionally. Sometimes we do things subconsciously, this is part of what happened with Gene.
Competition can threaten a friendship in much the way it threatened Finny and Gene's friendship. If one or the other of the friends is jealous of the other's success, the two friends can grow apart.
However, if both friends have the right frame of mind, competition can help a friendship. It gives the two people a sort of connection with each other. They can both strive to be the best they can be, while still hoping that the other keeps up with them. This will be especially possible if the two friends are closely matched -- they can each win some and lose some and keep pushing each other to improve.
Competition can threaten friendships in several different ways. Two students who are being pitted against eachother are secretly hoping that the other one will fail or make a mistake so that they can overcome them by the easiest method possible. If the physically (or academically) "better" person happens to lose, then they get into the habit of making excuses, etc...and that can damage a friendship very quickly. I've often found that contact sports can bring an "intent to injure" which can (from personal experience) can destroy a solid friendship.
Competition can help friendships out, as well. If two good friends are working with eachother on the same team and they happen to both excel, it can bring them both closer in that bond. Point in case is Colt McCoy and Jordan Shipley (QB and WR for the Texas Longhorns), they've been best friends since they were young and they were one of the most dominating forces in NCAA football.