Thank you for asking so respectfully, its really appreciated.
The truth is that everyone who is kin has a slightly different theory for how it is possible, but I will tell you the major ones.
Firstly, there is multiverse theory. You may be somewhat familiar with the idea of a multiverse if you’re acquainted with Marvel Comics or similar sci-fi stories. The idea of a multiverse is a real theory that states that for any possibility that can happen, there is a universe where it happens. Which if true, means an infinite number of universes where Lord of the Rings happens slightly differently- and the same for this world, and the same for any other work of fiction.
Many fictionkin believe that their existence is tied to the multiverse in some way, either because they lived a life as a character in another universe and were reborn in this one, or because they are living simultaneously in this universe and another, etc.
The other major conceptualization of how fictionkin are possible is the psychological model, which some kin follow. They believe that being kin is entirely mental- ie, it has to do with the way that their brain functions.
I will also tell you that the people who believe they are fictionkin didn’t just come to that idea spontaneously, or because they liked the character. Fictionkin discover who they are because we experience anomalous feelings, memories, urges and other phenomena that don’t have another adequate explanation.