Note: There are spoilers for the end of Final Fantasy XIII-2 ahead. Turn back lest ye be spoiled!
For those who never slogged through Final Fantasy XIII-2, a little background on Noel: he's from an apocalyptic wasteland 700 years in FFXIII's future, and goes back in time so he and Serah can "fix" the broken timeline. It is also completely his fault when the world is destroyed.
The player is told that he's friends with the main villain, Caius; we say "told" because they never behave in a friendly manner. Caius also wants to destroy the world, and is effectively immortal--his heart belongs to the Goddess (which can be taken in battle), and is the only thing keeping chaos from consuming the world. Noel, frustratingly, is unable to put those clues together the way the player does. Even when the player is given the option to kill Caius and take the heart, Noel refuses to go through with it. So when Caius predictably destroys it and brings about the apocalypse (and, spoiler, kills Serah), the player feels cheated: we could have saved the world, but we were stuck with a character that stupidly refused to follow through.