in general, fight club is a meditation on nihilism: everything will die, nothing will last, nothing makes sense, so how do we want to die?
passive nihilism ("team blue") is represented by the anonymous character, wasting his time to optimize his appartment (cave) with pretty-but-useless furniture, waiting for a day that never comes (false patience, hopium), waiting for "a natural death" (in effect, rotting in bed while being held alive by "doctors"), selfishly trying to "just have some fun" and then die without leaving a trace
active nihilism ("team red") is represented by Tyler Durden, the man with a plan... of course he will not change the fact that everything will die, but at least he actively consciously chooses to "die with style", to "die in combat", to die as a warrior, sacrificing his life for some higher purpose ("space monkey"...)
there’s more i won’t list
one detail i really like about fight club is the "homework assignments" scene, where Tyler Durden (the leader) assigns "homework" to his soldiers in written form, so all the operations stay as clandestine as possible. so effectively, Tyler Durden is bootstrapping his own secret service, biased towards "active measures" (team red, attack)