Willy totally believes in the social order he is part of, and tries vehemently to be a success within this system. Sadly, he cannot see that he is not equipped to succeed in the system he chooses to be part of, and he refuses to accept help to change the way he lives in order to survive.
For example, Willy has always worked to be a self-made man. He is a salesman, seeking out markets and striving for the commission which will help him support his family in the way he wants to. Willy has never really been able to succeed in this environment. In Act 1, we see him reminisce over returning from a sales trip. He tells Linda-
WILLY:..I was sellin' thousands and thousands, but I had to come home.
Linda rushes to calculate Willy's commission, and as she does this his story begins to change-
WILLY: The trouble was that three of teh stores were half-closed for inventory in Boston.
By the time we see him as a man in his sixties, he is even less successful. He is working on commission only and is 'borrowing' money from his friend Charley to give the illusion to Linda that he is being paid. Unfortunately, Willy's desire to succeed in the societal system he believes in means that he cannot take the job offer from Charley. This would be defeatist, and Willy would have to admit that he was not a good salesman - something he had striven to be for his whole working life.
Charley is exasperated with Willy's actions, but he wishes to support his friend-
WILLY: I-I just can't work for you, Charley.
CHARLEY: What're you, jealous of me?
WILLY: I can't work for you, that's all, don't ask me why.
Willy is contemplating suicide as we know, and yet he is unable to accept Charley's offer. This would be more of an admission of waekness than suicide? Willy seems to be conditioned to think so. He must support his family by himself, even if he has to die to do it.