Why does Finny invent a new game?

Blitzkrieg means "lightning war". Blitzkrieg was first used by the Germans in World War Two and was a tactic based on speed and surprise.

Blitzball is the game of the summer, invented by Phineas. It features no teams and places the odds against the ball-carrier, who must outrun every other competitor or be forced to relinquish possession to another participant, who, in turn, has the right to refuse the challenging task of being the ball-carrier. The game is a metaphor for the individual struggle of each student at Devon, who finds himself alone in a world without teammates, where conflicting emotions and desires impinge on the individual's success and well-being. Some, like Gene, grow weary and are tackled. Some, like Leper, refuse to even accept the challenge of carrying the ball. But Phineas alone excels at both the game and the game's metaphor: life as an adolescent about to become an adult. Finny is tireless and exuberant, surpassing every challenge and competitor, unafflicted by fear or lack of self-confidence.