In Death of a Salesman Biff Loman is the embodiment of Willy's inner hopes to give another go at life and, perhaps, undo his own failed attempts to make something out of himself. Biff, as an extension of Willy, is his eldest son and biggest hope. In the beginning, things go quite well; Biff is a high school football champion, has good looks, and demonstrates initiative, albeit, for causing mischief that Willy condones.
Willy and Biff feed each other's egos. While Biff gives Willy a hope for a better and flashier future, Biff feels happy to obey the life rules put forth by the most important and most admired man in his life: his father.
Yet when Biff discovers, one event at a time, that Willy's image is merely that, he shuts down and slowly realizes that his own life has also been a series of Willy-created fantasies.
But even in his delusional world, Willy still holds an amount of hope for Biff. Even though he knows that Biff is "lost" and cannot find himself, he consistently contradicts his feelings for Biff and ends up going back to seeing him with hopeful eyes.
Certain men just don’t get started till later in life. Like Thomas Edison, I think. Or B.F. Goodrich. One of them was deaf. [He starts for the bedroom doorway.] I’ll put my money on Biff. (Act 1)
Perhaps the hardest thing for Willy to accept is that he had everything to do with Biff's incomplete development. During his conversation with Charley's son, Bernard, Willy could not help but wonder how come Bernard found it so easy to find himself and make it in life whereas Biff did the exact opposite. It is here when he realizes that all things went downhill after Biff found out that his father had an extramarital affair. This is what starts the dysfunctional relationship between father and son and what will never be mended again.