Coraline's courage in the face of her fears is one of the main themes of the novel. She shows her bravery by returning to the eeriness and evil of the other world and other mother in order to save her own parents, and the black cat accompanies on the journey.

The cat shows courage in accompanying Coraline to the other side. Early on, Coraline conveys to the cat what she has learned from her father about courage:

when you're scared but you still do it anyway, that's brave.

The cat sneers at this but shows exactly this kind of courage in chapter 10. The cat seems bristling and angry, but is actually terrified because it knows, ahead of Coraline, that the two of them are going to have to face the other mother. As Coraline pets the cat, she:

could feel how hard its heart was beating. It was trembling like a dead leaf in a storm

The cat is afraid but doesn't run away. And when Coraline throws the cat at the other mother, it shows it courage by attacking her:

The cat made a deep, ululating yowl and sank its teeth into the other mother's cheek.

The cat is an alter-ego of Coraline and just like Coraline, shows its decency by acting bravely even when it is frightened.