Everett says he is the "paterfamilias" which is Latin for father of the family which can also relate to a leader. In this he is asserting his right to be Penny's husband since he has fathered all of their children as well as the decision maker. This relates to THE ODYSSEY in that Odysseus had to reclaim his lands and title after his long absence.
I believe that O Brother, Where art thou is, in essence, a movie about progress and history.
Like many aspects of the movie "O Brother Where Art thou", the title is an allusion of an allusion. The Coen Brothers themselves have been quoted as saying that the title references the fictional book of the same name in Preston Sturges' 1941 film Sullivan's Travels. In this earlier movie, John Sullivan, a movie producer, is on a search for a better movie based on the adaptation of the fictional book, "O Brother Where Art Thou". This title is itself an allusion to the novels of Steinbeck and ultimately even to the story of Cain and Abel in the book of genesis. In the Coens' movie, O Brother Where art thou, the characters are on a search for literal treasure. In neither of these movies do the characters find what they are looking for. The viewer too, may not find precisely what they are looking for. Indeed, if one expected to find a story as "fine" as Gulliver's Travels or one whose moral is as universal as the story of Caine and Abel, Sullivan's travels would fall short. As would any viewer be disappointed if they expected the movie "O Brother, where art thou" to be, as the character John Sullivan would, a serious movie that about the plight of the downtrodden. following the trail of these allusions places the viewer too on kind of treasure hunt, never ultimately finding what we are looking for.
The most overt allusion that the movie draws from, The Odyssey, seems conversely to give the viewer the most "treasure". Odysseus is there in the veil of Everett Ulysses McGill as are his shipmates and family. The angry gods make appearances, as do the sirens, the Cyclops and many more. However, the quality and scope of these characters seems to have degenerated throughout the ages. Instead of Odysseus (Ulysses in Latin) the great king overcoming great woes to guide his men home and return to his loving family, we are presented with Everett, a two-bit con man who fools his men into helping him return to his estranged family. The family too seems degenerate. Odysseus' wife is utterly faithful and goes to all length to fight off her suitors. His son is a brave prince who tries everything to find his father. Everett's wife Penny, on the other hand, is ashamed of her estranged husband. She lies to her daughters and tells them that Everett has been hit by a train, and plans to marry her "suitor". After seeing her, Everett even calls her a "succubus". The Coens seem to have gone out of their way to deprive the characters of "O Brother Where Art Thou" of any vestige of the heroism and greatness that their forebears once possessed. A one-eyed bible salesman has replaced the great Cyclops, the sirens are now just highway robbers and ancient Greece has become 1930's Mississippi. Even the comic narrative of "O Brother Where Art Thou" proves inferior in quality to that of the epic Odyssey. In framing their degenerate narrative in such sharp contrast to the heroic Odyssey, the Coens do more than invite comparison. They have re-formed the Odyssey and emerged with something poignantly less. In doing so, they seem to hint at the fact that reform is not synonymous with progress.
This idea is one that recurs again and again in the movie, but never as noticeably as in the side-story of Pappy" O'Daniel. Pappy, is the governor of Mississippi. Pappy is shown to be a fat autocrat. However, his opponent, Homor Stokes, the "reform candidate", is shown to be much worse. He is, in fact the leader of the KKK. We even find out that the nature of Homer's political reform is to combat racial integration in Mississippi. Again, we see the idea of reform leading to a reversal of progress.
One notable exception to this idea comes in the form of radio. No doubt, the radio represents a "reformation" of technology, and yet it also is a positive image in this movie. Everett and his men are helped in a way that Odysseus could not be by the power of mass communication. "The Suggy Bottom Boys" are first made famous by their songs on the radio and then later use radio to vanquish Homor Stokes. No doubt, radio is a prime example of how re-formation can be positive. "O Brother Where Art Thou" does not seem to present the idea of reform as strictly positive or negative. Instead, we are offered a different image: that of manic depression. This notion is made manifest in the movie by the character of Baby Face Nelson.
In the last scene of the movie, we are presented with an image of a flood washing away a valley. Everett explains that the entire state will be put on hydroelectricity, which will bring in an "age of reason" and put an end to "backward" ways. Indeed, the viewer knows that Everett's prophecy has come true. Since the 1940's America has been re-formed by electricity. However, given the ambivalence with which the movie treats the idea of reform, perhaps Everett's optimism is premature. It is ultimately left to the viewer to decide whether the vast reform of America brought about by technology is, like radio, a cultural progression, or else like the narrative of the movie itself, a step-backwards.