How we cite our quotes:
A terrible impulse to flee, to abandon Peeta and save myself, shoots through me. [...] I remember how I did just this when the mutations appeared in the last Games. [...] But this time, I trap my terror, push it down, and stay by his side. This time my survival isn't the goal. Peeta's is. (21.6)
In this instance loyalty trumps that other virtue, courage. Katniss could go out by herself and survive. That's her basic human instinct, which she deems a "terrible impulse." Deep down, her gut feeling is going to be to try to survive. Here, though, her loyalty is stronger than that. She owes Peeta and she's committed to him. That feeling is enough to get her to stay, to work for the survival of another person instead of herself.
That's when I remember the wire and how important it was to him. I look frantically around. Where is it? Where is it? And then I see it, still clutched in Wiress's hands, far out in the water. My stomach contracts at the thought of what I must do next. (23.54)
Katniss is willing to risk her life to save this wire, because she knows how important it is to Beetee. She trusts him enough to know that if he believes the wire has value, it must be the case. She has to be brave enough to swim into blood-drenched water and take it from the body of a dead woman. That's loyalty.
There is no question about it. For reasons completely unfathomable to me, some of the other victors are trying to keep him alive, even if it means sacrificing themselves.
I'm dumbfounded. For one thing, that's my job. For another, it doesn't make sense. Only one of us can get out. So why have they chosen Peeta to protect? What has Haymitch possibly said to them, what has he bargained with to make them put Peeta's life above their own? (23.74-75)
Here people are acting loyally when they shouldn't, at least according to reason. Katniss finds this behavior highly suspicious. The first thing people like Finnick and Johanna should do in the arena is take out weaker opponents like Peeta, but instead, they're "put[ting] Peeta's life above their own." This seems like putting off the inevitable since, as far as they know, by the end of the Games only one of them can still be standing.