The art of storytelling: Researchers explore why we relate to characters. For thousands of years, humans have relied on storytelling to engage, to share emotions and to relate personal experiences. Now, psychologists are exploring the mechanisms deep within the brain to better understand just what happens when we communicate. Source 6d.
Personally, if I choose a character I rather its my own invent rather than someone's like in a book or movie but since this topic is about that I will theorize. Basically, I think most of us like to identify with a character both because of the weakness and strengths of that character. I know many focus on the strengths but they secretly love the weakness because it gives us some normalcy in our own imagination.
I figure we all subconsciously wish to be better versions of ourselves. In today's capitalistic society very few have the power and luck to continuously improve their lives without setbacks or distractions. The vast majority of people live lives that they are less than satisfied with.. With this in mind it is only natural that so many people imagine themselves as other people or a character in a work of fiction. In the end it can be considered that the level of interest humans show in being a character in a story is directly correlated to their satisfaction or lack thereof of their current existence.