Death of a Salesman by Arthur Miller is a tragedy, and one of the greatest tragedies is the fact that none of the Lomans is unable to distinguish between reality and illusion.
Willy foolishly and erroneously believes that the most important thing anyone needs to get ahead in business and in life is to be good-looking and well liked. He has held to that belief all of his life, and it is not surprising that both his boys grow up to embrace that same philosophy. When Biff was in school, Willy was convinced that his son's popularity far outweighed his innate dishonesty (learned, of course, from his father). Of course this is an illusion, not the reality--even though it does seem to work for Biff for a time.
Later, we hear Biff express this same philosophy when he describes Bernard:
He's liked, but not well-liked.
Biff grows up to be petty, small-minded, and unsuccessful, at least in part because of this flawed thinking. He is thirty-four years old, yet when he gets turned down for a loan (rather to his surprise, again because of the philosophy Willy lived by and taught his sons) he churlishly steals a pen, pouting because his charm did not work.
Happy also lives as if his father's illusion were reality. He is the one who convinces Biff that he will undoubtedly get the business loan--as well as all the hot girls he could want. He tells his brother:
I bet he’d back you. ‘Cause he thought highly of you, Biff. I mean, they all do. You’re well liked, Biff. That’s why I say to come back here, and we both have the apartment. And I’m tellin’ you, Biff, any babe you want....
All of the Loman men live their lives under this illusion, which certainly contributes to their failures in life.
A second instance of appearances (illusion) not matching the reality in this play is the Lomans' marriage. Willy is not faithful to his wife, but he certainly keeps up the appearance of faithfulness to her. When Biff discovers it, the relationship between them changes; however, Linda knows nothing of the affair. The closest Biff gets to telling her about his father's unfaithfulness is to call him a "fake." Her response demonstrates her belief in the illusion rather than the truth (reality):
Why a fake? In what way? What do you mean?
She lives as if the illusion were reality; however, she probably should have known.
Finally, Willy really believes he is a successful salesman. He brags to his family, saying:
Some day I'll have my own business, and I'll never have to leave home any more. And they know me, boys, they know me up and down New England. I can park my car in any street in New England, and the cops protect it like their own.
The reality is that he is not a successful salesman, and things have gotten worse in the last few years. His territories have been given to more productive men, and yet Willy is unwilling to change his thinking or his philosophy, blaming his lack of success on other people:
You know, the trouble is, Linda, people don't seem to take to me.
While that is probably true, it is not the cause of his declining sales ability. Linda knows it and his sons figure it out, as well. When Willy finally figures it out, he no longer wants to live.
Once Willy does finally face the reality that he is a failure and is worth more dead than alive, he no longer has a reason to live. His final act of suicide is really his only success in the play, as he is able to provide his family with something that, in life, he could not give them.