First, in order to make sense of Fight Club we need to remember that the whole movie is from Jack's (the narrator) perspective. When you watch the movie you are not seeing events as they happen but rather as Jack remembers them happening.
This means that whilst there is fact in his story there can also be fiction and even events that defy logical explanation. After all we are acrually watching Jack's memories and we all know he has some mental issues.
So, having accepted that we can now look afresh at the events he retells and interpret them in this context. Some examples;
- Tyler's physical appearance. If we were seeing events as they happened we could never see Tyler as he is simply Jack's alternate personality.
- The Paper Street Mansion. As is widely accepted in theories, the Paper St Mansion exists only in Jack's head. We could never see the physical building as it does not exist. If we were watching events as they happened then we would see Jack's actual location whilst he described the masiin and the events that take place there.
- The carpark fight. It is not phsically possible for Jack to drag himself through the carpark in the way we see it on the security footage. Rather Jack is describing what he thinks it would look like now that he understands Tyler is not a physical being.
So, what is my theory then. Very little of what we see in the movie happens in the physical world. In fact the only scenes with any grounding in the real world are those where Jack's physical presence is observed at work. That's right, pretty much every scene and every character exists in Jack's head only. There is no Bob, no Marla, no support groups, no Project Mayhem, NO FIGHT CLUB. Everything and everyone outside of his work is created in Jack's mind only.
So what is it all about then? Carefull thought reveals the narrative is actually a recounting of the fight for power and control within Jack's mind. Tyler is making a bold play to dominate and take control. To do so he must befriend Jack, the one currently in control, and subdue all others such that they will not challenge him when he wrestles control from Jack.
Jack has many other strong personalities such as Bob and Marla who Tyler seeks to overthrow by having Jack forget them. In forgetting them they die. And when Jack remembers them and they enter the narrative again Tyler subdues them as he has all the other personalities Jack has created.
The ending then, where Jack shoots himself is not a physical occurrence but rather a symbolic reference to Jack forgetting Tyler and therefore Tyler is dead.
There is much more to be said for this theory and I will eventually provide far greater detail but for now let the conversation continue.