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Here's a thought: The Big Lebowski is all about the penis. The dick, the rod, the johnson.
More specifically — and not to get all grad thesis on you — it contemplates the projection of masculinity versus the penis itself. The former, of course, is represented by Jeffrey Lebowski, the Big Lebowski of the film's title, confined to a wheelchair and obsessed with outward displays of power.
The penis itself — alternately hard and soft, giver of life? That's exemplified by the other Jeffrey Lebowski, the Dude.
The Big Lebowski is a braggart and a blowhard, his house decorated so ostentatiously that the Dude jokingly asks if he can move in. In truth, however, the Dude isn't impressed with Lebowski's tokens of power, though he does help himself to one of his rolled-up rugs. Phallic-symbol alert.See also: Jackie Treehorn's House and Its Eccentric Owner
Enter Bunny, Lebowski's trophy wife, played by Tara Reid and young enough to be his daughter. All signs point toward a sexually unsatisfied relationship between her and her disabled, elderly husband. It seems that he desires her not for the act of coitus but to project an image of vitality to the outside world. Indeed, while it's not uncommon for paraplegics to have active sex lives, the leg wound is a long-standing symbol for sexual impotence in literature (see the Fisher King). She promptly leaves him.See also: Top Five Most Exciting Lebowski Fest Moments
The Big Lebowski does have, of course, an actual daughter, Maude, a conceptual artist played by Julianne Moore, who disapproves of his lifestyle just as he disapproves of hers. The two never interact in the film; he never mentions her. Thus, while he is able to physically produce a child (or at least once was able), Lebowski cannot fulfill the function of a father. In fact, he can't even provide for her, and it turns out she's actually floating him financially. He also steals money from his metaphorical children, the Little Lebowski Urban Achievers. This forces Maude to protect him, and further inverts the parent-child dynamic.