[Opening credits inside the human body. Camera travels through nerves and blood vessels, before coming out through the pores in the main character's skin.]
The movie literally starts inside our main character, with a computer-generated title sequence sweeping through his vessels and organs. That's a way to explore him physically, and the rest of the movie is about exploring this guy mentally.
NARRATOR: I know this because Tyler knows this.
This line is our first clue that our narrator and Tyler are the same person. Without knowing this, you assume they're just really close buddies. They tell each other everything. But the line takes on a whole new meaning once you know the twist.
NARRATOR: People are always asking me if I know Tyler Durden.
Contrasting with the last line, this line throws us off a bit as to the narrator's identity. Why would people ask him if he knows Tyler Durden if he is Tyler Durden? Of course, we later learn that most people in other cities don't know what Tyler Durden looks like.
NARRATOR: It must have been Tuesday. He was wearing his cornflower blue tie.
People in the corporate world define their identity by their clothes. Our narrator's boss, who is the antithesis of who our narrator wants to be, marks every day with a different tie.
NARRATOR: What kind of dining set defines me as a person?
Our narrator may have just disparaged his boss in that last quote, but he is very similar: he defines himself though material objects, not through actual accomplishments.
MARLA: It doesn't have your name. Who are you? Cornelius? Rupert? Travis? Any of the stupid names you give each night?
Marla is onto our narrator early, calling him out on the fact that he wears a different name tag to each support group. We later learn that none of these is his real name.
TYLER: Who is this? NARRATOR: Tyler?
Listen to the dialog here, and you can imagine that Edward Norton is saying "Tyler" without a question mark, answering the question not with a question, but with a truthful answer. "Who is this?" "Tyler."
Sometimes Tyler spoke for me.
This reminds us of "I know this because knows this." Tyler speaks for him because he's telling him what to do…from inside his head. The scene at the hospital is like something from The Sixth Sense. No one actually looks at or responds to Tyler. And no, you're not seeing dead people.
NARRATOR: That was not a bunch of stuff that got destroyed. It was me!
Our narrator's identity was composed of IKEA furniture instead of accomplishments, hopes, dreams, failures, and fears. When his apartment blew up, his entire identity blew up with it, and he had to rebuild it from the ground up.
TYLER: Stickin' feathers up your butt does not make you a chicken.
This is a funny line, but also one with meaning. Tyler is saying that you can't just talk the talk, you have to walk the walk. There is no "fake it 'til you make it." If you're faking it, you're just fake.