It's important to remember that Walter's initial attempt at contact with George is friendly, though it occurs in a rather eccentric circumstance.
In Act II, Scene One, George enters the apartment to pick Beneatha up for a date. Meanwhile, Beneatha and her brother are in the middle of mimicking what they consider to be an African ceremonial dance. Walter sees George, "extends his hand for the fraternal clasp," and is rejected when George exclaims, "Black Brother, hell!"
It also becomes clear from the dialogue between George Murchison and Beneatha that George is not interested in joining the wave of Afrocentrism that appeals to Beneatha. He is initially put off by her short, natural hair. He is also dismissive of black culture generally: "Let's face it, baby, your heritage is nothing but a bunch of raggedy-assed spirituals and some grass huts!"
Due to his snobbishness and his apparent self-hatred, it is rather easy to see George as unlikable. Walter, too, dislikes George, but also feels inferior to him due to the latter's education and airs of sophistication. For example, when George talks about theater conventions in New York and mentions, offhandedly, that he goes there several times a year, Walter dismisses the city, then lies and says that he, too, has been.
Walter then scrutinizes George's attire: a "casual tweed sports jacket over cashmere V-neck sweater over soft eyelet shirt and tie, and soft slacks, finished off with white buckskin shoes." It is an outfit that perfectly symbolizes Walter's derisive epithet: "Eastern." Walter refers to the shoes as "faggoty-looking." Because he cannot match George intellectually or culturally, his defense is to attack the young man's masculinity. He dismisses George's pursuit of the education Walter could never have:
I see you all the time—with the books tucked under your arms—going to your (British A—a mimic) "clahsses." And for what! What the hell are you learning over there? Filling up your heads...with the sociology and the psychology— but they teaching you how to be a man? How to take over and run the world? They teaching you how to run a rubber plantation or a steel mill? Naw—just to talk proper and read books and wear them faggoty-looking white shoes...
Walter, in this brief monologue, positions himself as a man of action, a man who is only interested in pursuing capital gain. On the other hand, in Walter's imagination, George is pretentious and wasteful of his time and energy.
When George characterizes Walter as "bitter," Walter acknowledges that as true, and uses George's criticism to seek a point of connection:
And you—ain't you bitter, man? Ain't you just about had it yet? Don't you see no stars gleaming that you can't reach out and grab?
George ignores this plea for empathy and "crosses to Beneatha." He even changes his mind about her hair, after Walter registers his disapproval of her new cut.
The exchange with George reveals Walter's worst traits—his enviousness, his pettiness, and his covetousness. However, the dialogue also reveals his vulnerability. He wants to connect with George, the only black American male in the play who possesses some of the things that Walter wants. However, George, out of his own need to distance himself from Walter and what Walter represents, rebuffs him. George, in fact, ends the exchange by saying, "Goodnight, Prometheus," and exits the apartment. Walter is confused by the association and, instead of acknowledging that he does not know something, accuses George of being unable to "insult [him] man to man."
The exchange represents not only Walter's insecurities, but also the ways in which poor and middle-class black people have failed to connect; and how some middle-class black people have used their educations to dismiss poor blacks instead of helping them.