You might not have to offer "arguments" about loneliness in Steinbeck's book. It might be simpler to offer three examples of loneliness. Then if you feel there is a need to argue about anything, you might use that in your conclusion. Personally, I don't see that there is anything to argue about, although there are good examples of loneliness.
The loneliest character in the book is Crooks, whose pitiful situation is described in the opening of Chapter 4. He is forced to live by himself because of racial prejudice. He is further handicapped by being badly crippled. He copes with his loneliness by reading.
In contrast to Crooks, Curley's wife is the next loneliest character. She is white, young, and attractive, but the men are all afraid to have anything to do with her because she is the wife of the boss's son who could get them fired, and also because she is "jail bait," meaning that she is a minor. She is restless and capable of causing trouble because of her loneliness. Her loneliness actually causes her death when she becomes too friendly with the apparently harmless and simple-minded Lennie.
For a third example, I suggest you use the little story George tells Lennie in the first chapter. Although it comes first in the book, it might be most effective if used at the end of your essay. (It's always a good idea to save the best for last.) Here is what George tells Lennie in Chapter 1 while they are sitting by the campfire:
"Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don't belong no place. They come to a ranch an' work up a stake and then they go inta town and blow their stake, and the first thing you know they're poundin' their tail on some other ranch. They ain't got nothing to look ahead to."
This is mainly what Steinbeck's book is about. The men who live in the bunkhouse are all loners. They have no loved ones, and their only possessions are the few things they can roll up in a blanket and carry on their backs when they either want to or are forced to move on. They may not even understand that they are lonely. George seems brighter and more philosophical than most of them. It is he who realizes that "Guys like us, that work on ranches, are the loneliest guys in the world."
Steinbeck was a compassionate man. He truly felt sorry for the kinds of underprivileged people he writes about, and he makes the reader share his feelings.
You may wish to argue that the historical setting of the Great Depression generated first the disenfranchisement of many workers which, in turn, led to loneliness as men had to become itinerant and leave their homes. Then, the fear of others competing against them for the same jobs kept men alienated from one another. And, thirdly, the alienated and lonely lives that men lived in the 1930s resulted in their becoming cruel to one another.
Here, then are some ideas to help you get started (You will want to find supporting details for these points):
- Disenfranchisement leads to loneliness - In contrast to the other bindle stiffs, George and Lennie travel together, mainly because George has promised Lennie's Aunt Clara that he will care for the mentally challenged man. Theirs is not so much a friendship as a symbiotic relationship: George is the brains and Lennie the brawn. The other ranch workers have no friends as they are strangers to one another. Curley is separated from the others by virtue of being the boss's son, and Slim must remain somewhat aloof as the mule skinner. Crooks, the black stable mate is marginalized by his color.
- Fear of others leads to alienation - Old Candy worries that he will be fired when he is no longer useful and able to swamp out the bunkhouse: "Jus' as soon as I can't swamp out no bunk houses they'll put me on the county"; Crooks worries about the racial prejudice of the others: "They play cards in here, but I can't play because I'm black. They say I stink"; and all the workers fear Curley's anger since he is the son of the boss. After he challenges Lennie, George tells Lennie, "Ya know, Lennie, I'm scared I'm gonna tangle with that bastard myself...."
- This alienation and loneliness leads to cruelty among the men. Curley becomes pugnacious and Whitson wants to shoot the old dog of Candy. When Lennie comes into Crooks's room, the stable mate is cruel to him, telling Lennie that George might not return, ""...s'pose George went into town tonight and you never heard of him no more.....S'pose he gets killed or hurt so he can't come back."