Martin and Barresi (see my post 'The ghost in the machine') draw attention to Nietzsche's brilliance in seeing so clearly and so early (his final mental breakdown occurred in January 1889) the questionable nature of the self. (The quotes are from pages 194 and 195.)
'Nietzsche is famous for having proclaimed that the rise of Enlightenment secularism meant that "God is dead." He is virtually unknown for having uncovered, in his personal reflections, the perhaps deeper truth that the self is dead ...
"Everything that enters consciousness as 'unity'," he said, "is already tremendously complex." Rather than unity of consciousness, we have "only a semblance of Unity." To explain this semblance, rather than a single subject [or 'I'], we could do as well by postulating "a multiplicity of subjects [or 'I's], whose interaction and struggle is the basis of our thought and consciousness in general." We do not have any reason to believe that there is a dominant subject overseeing this multiplicity. "The subject [or 'I'] is multiplicity." '
(This view, by the way, is in accord with my understanding of the best recent neuroscientific theories.)
'Nietzsche concluded,' write Martin and Barresi, 'that we have been victimized by our language, that is, by "our bad habit ... of taking a mnemonic, and abbreviative formula, to be an entity, finally as a cause, e.g., to say of lightning "it flashes." Or the little word "I." To make a kind of perspective in seeing the cause of seeing: that was what happened in the invention of the "subject," the "I"!" '
In other words, Nietzsche is saying that we have bought into the fiction of thinking that if there is a flashing, then there is a 'something' - an 'it' - that flashes; and if there is seeing, there is a 'something' - an 'I' - that sees. But this 'thing' that does the flashing does not exist - lightning is an electrical phenomenon in the atmosphere; and likewise the thing that does the seeing is not an internal agent, the 'I', but the physical organism (comprising eyes and brain, etc.).
So the "I" - or self - is neither a single thing, nor an agent (it does not do anything). Is it a fiction?