It's not that rough ridin' hard, people. The Hound and Arya were both using each other to accomplish their goal(s). The Hound sought money and reprieve from Stark sympathizers, as he had burned his bridge with the Lannisters. Arya sought safety and revenge. Over the course of their story arch they began to relate to each other on some levels, but neither actually developed the sort of relationship that is being suggested here. Arya still said his name in her prayer every night before going to sleep and Sandor was well aware of this.
Arya chose not to kill The Hound, as she did not want to give him the satisfaction of a quick, painless death. She thought this was the appropriate form of justice. It's not that rough ridin' hard to understand. Arya wanted safety, then revenge. The Hound wanted money and clemency.