In what ways does the ideological conflict between Willy and Biff become obvious in Death of a Salesman?
When Biff tries to get a loan from his old boss and is rejected, he realizes an important fact about his personality. He realizes that he has been fooling himself; deluding himself with an over-inflated self-concept.
Coming to a new view of himself, Biff comes to a new view of his father. Initially, Biff's emotional state is one of resentment, but Linda convinces Biff that Willy is in emotional trouble of his own.
Biff tries to bridge the gap that has opened between himself and his father by telling Willy that he is not angry anymore and that he accepts his personal failures as his own. He doesn't blame Willy.
When Willy hears this, he only hears another attack from Biff, leading Biff to fully articulate the intellectual difference between the two of them.
"You were never anything but a hard-working drummer who landed in the ash can like all the rest of them! ... I'm nothing, Pop. Can't you understand that? There's no spite in it any more. I'm just what I am, that's all."
Willy insistently clings to a view of himself as a "somebody"; a person of importance. This delusion, once shared between Biff and Willy, Biff now rejects. Willy, however, will not or cannot make the admission Biff makes.
This difference between the two men is seeded earlier. Biff accepts failure early on when he chooses not to take a summer school course so that he can graduate from high school. He also is forced to recognize that Willy is a fraud when he stumbles onto Willy cheating on Linda in a Boston hotel room.
As we know from Act I, Part 4, Willy threw Biff out of the house because Biff knew he was a “fake.”
Though Biff's belief in Willy's virtue ends with that episode, Willy goes on imagining that he can or should be great like his brother Ben.
From the conversation in the restaurant announcing the failed attempt to get a loan to the end of the play, Biff tries to convince Willy to accept him as he has accepted himself so that they might deal with one another honestly.
Too desperate or too deluded, Willy refuses to understand the point Biff tries to make.