The Big Lebowski Analysis

The characters are idiosyncratic.
There's a general lack of lack: The Dude seems to be rather content with his life. Balanced. He is the ego. John Goodman's character, Walter could be seen as a representation of the superego. The father figure that strives to enforce his morals onto others.  The Dude seems rather easily impressionable, e.g. when he is seen to be doing something resembling tai chi he is essentially just copying an interpretative dance which he saw earlier, he doesn't really practice tai chi. The dude also says the same line he heard the president say on the television to the other Lebowski.
The Dude is a  pacifist, as is even recognised by Walter in the film. this sensibility indicates his role as the Ego trying to find a peaceful resolution.

As according to Roger Ebert: "The film is about an attitude not a story. The focus should be upon how the characters react to their circumstances and what we can learn from such."

The film is arguably a film about literal and figurative castration:

1. When one says figurative castration it means the idea of a man feeling as if he is losing the qualities that he believes makes him a man. Walter see's himself as manly: toting firearms and talking about war-service in Vietnam. But he is still a servant to his ex wife: he takes care of her dog, he keeps to her religion (despite the fact that he was raised catholic and only converted to appease her family). 
2. The Big Lebowski (Jeffery, the millionaire, not The Dude), likes to present himself as powerful despite being impotent from the waist down, he has a trophy wife who is beyond his control and his daughter is really the one who runs the show.
3. Jackie Treehorn, the pornography boss says that the most erotic part of the human anatomy is actually the mind: presenting himself as some kind of enlightened smut mogul. But seconds later, The Dude learns that Treehorn likes to draw pictures of men with big penises, in fact, penises and ridiculous acts of bravado are everywhere in this movie; Woo even urinates on The Dude's rug: marking his territory - every male is a little insecure in The Big Lebowski (similar to Fight Club).
4. Conversely Maude is depicted as a powerful mythological figure in The Dude's dream, whereas he is a run of the mill man with no real sway of what happens to him. 
5. As for literal castration, it is mentioned frequently and threatened multiple times. When he comes in conflict with the nihilists, in order to get what they want, they say that they will otherwise cut off his penis, this is repeated with an echo effect and is laughed about by the nihilists as they walk away. Later The Dude, Walter and Donny discuss this matter at the bowling alley. Walter is terribly upset by this, Donny seems confused and The Dude is naturally concerned about his own penis.
6. In another scene, The Dude has a dream about the nihilists chasing him down with giant scissors. Suggesting they're about to make good on their threat. Theirs even a scene earlier with a giant pair of scissors in Maude's studio. The dude even appropriates this threat for himself when he needs to convince a young boy to give him back his money.
7. For further evidence, the word "man" comes up over and over in the movie. By way of repetition, this is intended to put the words into our mind.