What is the importance behind the development of a split personality?

It is revealed that in both "Murders in the Rue Morgue" and Fight Club, that the two main character depicted, the narrator and their partner in crime, are actually the same person. In both works the narrator does not actually do much, but then they both have this other who essentially drives the plot and makes things happen. Their other is everything they want to be, but are not. What drives someone to have to create an alternate personality instead of just working to build the characteristics that they want to attain? Do they have any control in the matter or is the development created out of trauma or a break in the human psyche?

I think that the development of an alternate personality actually reveals that the qualities that the person thinks they are lacking which they personify into this new personality, is within them all along. The only way that they believe that these qualities can emerge is by creating an alternate self. Still they have the qualities they were yearning for all along. This logic actually reminds me of a story I read when I was younger. A rabbit wanted courage and the Sky God said he had to complete these 3 tasks in order to get it, but in order to do the 3 tasks he needed courage. By actually doing the tasks, he reveals that he had the quality all along. Just in the situation with split personality, the quality is within.