In The Hunger Games: Catching Fire Katniss insisted Peeta must live. She also convinced Haymitch that he should protect Peeta at any cost. Why?
Pure and simply, Guilt.
Katniss feels guilt for many things in her life.
She feels guilty for leaving her sister alone with her mom as she was pulled into the Games. She feels that she is the provider to her family since her father died, and when she can no longer do that, she feels guilty for not being able to support them anymore (she assumes she will die in the games).
She feels guilty for getting Pres. Snow so ticked off at her and Peeta. She feels guilty about everything ... even though she has no control over any of it. She has a huge guilt complex which rules her life and everything she does.
She has grown an attachment to Peeta (not really love, but something close to it). If she doesn't do everything in her power to keep Peeta out of the games and safe, she will have more guilt. She is trying to keep herself from this, but ultimately fails.