Quote 1
'I want everyone watching – whether you're on the Capitol or the rebel side – to stop for just a moment and think about what this war could mean. For human beings. We almost went extinct fighting one another before. Now our numbers are even fewer. Our conditions more tenuous. Is this really what we want to do? Kill ourselves off completely? In the hopes that – what? Some decent species will inherit the smoking remains of the earth?' (2.56)
In this speech, Peeta asks for the fighting to stop. Other context in this chapter reveals that these aren't Peeta's ideas, but President Snow's – Peeta is being forced to speak for the Capitol. If the fighting stopped, the rebels would be destroyed. However, Katniss seems to realize that Peeta might mean the opposite of what he's saying here, that the rebels should fight, and that she should step forward to lead them.
Quote 2
"Who cares? He's dead, isn't he?" Tears begin to run down Peeta's face. "I didn't know. I've never seen myself like that before. Katniss is right. I'm the monster. I'm the mutt. I'm the one Snow has turned into a weapon!" (21.5)
Imagine what it's like to not even be able to trust yourself; to think you're fighting for one side when you've already been "turned into a weapon" by another. That's the situation Peeta's been placed in. It's hard for him to even know who he is any more, and it's terrible to realize that he's endangered other people on the rebels' side – he's no longer just a person but also a walking weapon.
Quote 3
"I think... you still have no idea. The effect you can have." He slides his cuffs up the support and pushes himself to a sitting position. "None of the people we lost were idiots. They knew what they were doing. They followed you because they believed you really could kill Snow." (23.54)
Once again Katniss has underestimated the power and authority she holds – "[t]he effect [she] can have." She's a dangerous warrior whom other people trust and put their faith in, a person whom other people are willing to die to protect and serve. She's a real, natural leader in ways that people like Snow or Coin never will be.