GC doesn't want to play Chaminade because they dont want to do anything to draw attention to Chaminade or create a legitimate rivalry. Each year they lose several good players to Chaminade and the more they try to make Chaminade irrelevant the less likely (they think) kids will leave GC. The last thing they want is to lose to them, I can promise you, but it is really more about just not showcasing Chaminade in front of future players.