Why do they kill people in hunger games for holding up three fingers?

In "The Hunger Games," holding up three fingers is a gesture of respect and farewell in District 12, often used to honor someone who is about to face death. When Katniss Everdeen does this during her tribute ceremony, it becomes a symbol of rebellion against the oppressive Capitol. The act is seen as defiance, and thus, in the context of the Games, it can lead to severe consequences, including punishment or death for those who display such resistance. The gesture signifies solidarity and hope among the districts, making it a powerful but dangerous symbol.