Here's my theory:
The doppelganger premise is a metaphor. The two men represent the double life of one man: a history professor with a pregnant wife, who visits sex clubs, is a serial cheater and has a mistress (The "actor" lives with the wife because the philandering necessitates constant lying). The spider is a metaphor for his wife, who makes him feel trapped; while the totalitarian state is the flipside metaphor for his double life (i.e. a system of lies that is consuming and destroying all aspects of his identity). He is scared of this side of himself, but he can't escape it. It has taken control of the whole person. The professor is a dazed cipher who is discovering his own life like an outsider looking in.
The cornered spider at the end is actually the beginning of the story, as he turns the tables on his "captor" with a lie and "escapes" to a world of sexual freedom (represented by the stripper stepping on the spider). The car crash with his mistress is the apotheosis of his lies and recklessness.
Although its based on a book, so this is probably all demonstrably wrong.