“Why did you do it anyway?” he says.
“I don’t know. To show them that I’m more than just a piece in their Games?” I say.

In this snippet of conversation, Katniss replies to Peeta when he asks why she decided on her blatantly rebellious demonstration to the Gamemakers. Notably, the quote recalls something Peeta said in the first novel of the series before he and Katniss competed in the Hunger Games. In that instance, he was saying he didn’t want the Games to change his character and change him into a killer. He wanted to maintain his integrity and humanity. It was a form of rebellion against the Capitol and the Games, which dehumanize the tributes by turning their slaughter into entertainment. Katniss echoes that rebellion here, though her reasoning is different. What she did in her demonstration was pretend to hang a dummy with the name of the previous Head Gamemaker, Seneca Crane, written on the front. Seneca Crane was executed after Katniss’s and Peeta’s suicide stunt at the end of the Games, and the act was intended to remind the Gamemakers of his fate and suggest that they could suffer the same. Katniss’s act, in other words, was an attack on the Gamemakers and wasn’t about maintaining her personal integrity.

Maybe more importantly, it was also intended to show them that they couldn’t control her. The Capitol strictly regiments everything that occurs in Panem using the threat of violence to keep people in line. The Games are perhaps the best example. They exist to remind the districts that the Capitol can crush them at will and to make them feel powerless. It’s that control that Katniss and many of the people in the districts rebel against. Katniss’s demonstration showed that she wasn’t afraid of displease them and displayed a contemptuous disregard for their control. When Katniss tells Peeta she did it to show them she’s more than a piece in their Games, she means quite literally that she wanted to make it clear that they can’t determine how she behaves.