* Protecting Rue: In the Games, Katniss kills a boy tribute from District 1, leaving his younger sister Rue orphaned. As a way to honor Rue's memory and protect her from further harm, Katniss invents the story of how she "won" the goat in a lottery. This creates the impression that the goat was already hers and Rue's death was not a consequence of her actions.
* Maintaining her image: Katniss is already a symbol of defiance and strength for the districts. She knows that admitting she killed the boy would make her appear ruthless and even make the Capitol suspicious of her true intentions. The story of the goat allows her to present a more innocent and compassionate image.
* Protecting Peeta: Katniss's fabricated story also helps shield Peeta from the consequences of her actions. The Capitol has been trying to pit Katniss and Peeta against each other, and admitting to killing the boy could have jeopardized their relationship and damaged their "star-crossed lovers" image.
* Manipulating the Capitol: By presenting herself as an innocent victim of the Capitol's cruelty, Katniss subtly undermines the Capitol's authority. The story of the goat serves as a reminder of the Capitol's ruthlessness and highlights the injustices that the districts suffer under their rule.
Ultimately, the story of the goat allows Katniss to retain control over her narrative and exploit the Capitol's manipulation for her own purposes. By creating a fictional backstory, she protects herself, her allies, and the districts from the Capitol's wrath while simultaneously fueling the rebellion.