Final answer:
Katniss Everdeen refuses to cry on stage when she volunteers to show strength and defiance against the Capitol's expectations, and to maintain a brave front for her family and the other tributes.
Step-by-step explanation:
Katniss Everdeen refuses to cry on stage when she volunteers for tribute in The Hunger Games because she wants to maintain a sense of strength and control in a situation where the tributes are typically seen as weak and powerless. By refusing to show her tears, she is defying the Capitol's expectation of how a tribute should behave, thus representing rebellion and resistance. Katniss understands the importance of keeping a brave front for both her own sake, to stay focused and strong in the games, and for the viewers at home in District 12, especially her family, to reassure them and not to show vulnerability to the other tributes.