I came up with the idea that in Fight Club the penguin and cave is introduced to create the idea of an imaginary friend that represents the narrator's aspirations. When Tyler tells the narrator the truth of them being the same person, he says "I most importantly am free in all the ways you wish to be". Is Tyler Durden the narrator's spirit animal?
It's an interesting theory, and the logical answer is: we can not know. We can not know because it is never explicated. But, on the other hand, it is quite evident.
The woman leading one of the support groups Fight Club's narrator attends, leads him to his power animal:
"Now we're going to open the green door. The heart chakra. .. Imagine your pain as a white ball of healing light. It moves over your body, healing you. Now keep this going, remember to breathe, and step forward through the back door of the room. Where does it lead? To your cave! Step forward into your cave. That's right. You're going deeper into your cave, and you're going to find your power animal."
I interpret the protagonist's power animal telling him (to) 'slide' meaning that deeply within himself the narrator wants to be able to just let go and enjoy the ride, fearlessly going where he may.
"All the ways you wish you could be: that's me. I look like you wanna look; I fuck like you wanna fuck; I am smart, capable, and—most importantly—I am free in all the ways that you are not. [..] Little by little, you're just letting yourself become ..Tyler Durden."
If the penguin is indeed the narrator's spirit or guide animal, Tyler Durden seems to be the physical and realistic manifestation of the attitude it represents. In the narrator's time and society, Tyler is the practical expression of this primal life force.