In "The Black Cat," the narrator states that he doesnt expect the reader to believe his story. So why does he say he is telling it?

When at
the beginning of the story the narrator says that he neither expect(s) nor solicit(s) belief,
he, or rather the author, is doing so as a way to build up the reader's anticipation of the
story to come. The implication of the narrators assertion is that the story is very bizarre and
unbelievable. The reader will thus anticipate an extraordinary story and will be keen to read on
and discover for themselves whether it is believable or not.

He subsequently
explains that he is telling the story because he expects to die to-morrow and wishes to
unburthen (his) soul before he dies. This implies that the story which the narrator is about
to unfold weighs heavily upon his mind and perhaps even upon his conscience. He wants to tell
the story now so that he can be rid of it and die with a clean conscience and a peaceful soul.
In this way, the process of telling the story is, for the narrator, a kind of or, to use a
rather crude , like an exorcismwhereby he can rid himself of demons which are a burden upon his
soul.