In the movie *True Grit* (2010), second to last scene, where Cogburn rides with poisoned Mattie.  
In the desperate attempt to save Mattie from the snake venom, Cogburn rides her (of Mattie) horse day-and-night to quickly reach a doctor. As I and everyone can imagine, the horse gets very tired in this race against the time.  

Question is: why does Cogburn decide to kill the horse instead of simply leaving it in the wild?