Psychologists have analyzed what draws us to other people, and have come up with several broad categories that determine our friendships with other people. A couple of those that apply to Gene and Finny's friendship are complementarity, utility value, and ego-support value.
Complementarity refers to the fact that we like to be friends with people that are different than us, but that work well with our personalities. I like to think of it as peanut-butter and jelly--totally different toppings, but together, they work really well. Gene is quiet, studious, serious and calm, whereas Finny is spontaneous, funny, charismatic and excitable. But together, they balance each other out. Finny helps Gene to get out of his shell, have fun and make friends, and Gene helps Finny to stay grounded and realistic. It's a good match.
Utility value refers to the fact that we often make friends with people who are useful to us for some reason. This also applies to Gene and Finny. Gene helps Finny to study and pass his classes, and Finny helps Gene to get out and relax every once in a while. They are useful to one another.
Ego-support value refers to how we like friends that boost our egos and give us a lot of support. Finny makes Gene feel good through complimenting his smarts, and bringing out the best in him, and Gene makes Finny feel good through being there for him in his games and antics.
For these three reasons, and many more, Gene and Finny make a friendship that really works; they complement each other, help each other, and support each other. I hope that those thoughts helped; good luck!