A lot of fanfiction writers start up because of their passion for a show. While any number of things can be the source of passion, a very common fixation is on one of the primary characters. So they start to write something because of their passion for this character, but they find something about the character that doesn't mesh well. Maybe they're the wrong gender or are otherwise not close enough to the author's expectations. (Or they want to make the character really, really cool even if they like the character as he or she is.) Or, alternatively, the author wants to pair their favorite character up with somebody, but "nobody is good enough for them". In any case, rather than put them through the Possession Sue process, they just get a Clone-O-Matic and out pops a Copy Cat Sue.