The Suicide Society was a club of Finny's invention, and was subject completely and totally to his spontaneous whims. It met every night, and initiation was jumping from the tree. The boys met, they played random games with random rules, and had a lot of fun while doing so. Blitzball was one of those games, and the rules were totally made up by Finny, and subject to changing at any time. Now, one might think that this would be total chaos, but, with Finny at the helm, it ended up being a lot of fun because he was very talented at including everyone and making them feel personally involved in the venture. Also, Finny was just so good at the game that it was pretty amazing to watch him dodge and weave--it was perfectly suited to his skill set. Gene describes,
"He had unconsciously invented a game which brought his own athletic gifts to their highest pitch...Phineas was driven to exceed himself practically every day...he created reverses and deceptions and acts of sheer mass hypnotism."
This reflects Finny's character also--he seemingly effortlessly and gracefully hypnotized those around him, and drove those around him to new tests of patience, but always with charm and success. He went with the flow, but always challenged himself, and above all, had fun doing it.
Gene didn't like the Suicide Society, or blitzball. In fact, he states rather darkly, that he never felt like going to any of the meetings, but he never said so. He hated jumping from the tree, and the haphazard rules of Finny's games frustrated and intimidated him. If Finny knew this, he probably would have been concerned, but convinced Gene in the end that he really DID like the meetings and the games, and Gene wouldn't even know what hit him; that is just how Finny was. Utterly convincing in a non-threatening way.
I hope that those thoughts helped; good luck!