In Death of a Salesman, please help me explain the situation with Willy being interested when Biff mentions Bill Oliver as to why they argue.
The part of the play Death of a Salesman that features the argument between Biff and Willy Loman over Bill Oliver occurs in Act 2, scene 5. However, the situation has a different origin.
Willy Loman is interested when Biff mentions Bill Oliver because the latter used to be a supervisor of Biff's many years ago when Biff was younger. Bill Oliver is a successful businessman. That fact alone is enough to get Willy Loman interested. However, this is a businessman for which Biff once worked and (in typical Loman fashion), Biff was thought to be, not the clerk that he was, but an associate of Oliver's. In Willy's mind, Biff was following every mandate and idea of success that Willy had bestowed upon him.
The problem is that Biff stole from Bill Oliver in the past. As a result, he quit working for him. However, the tendency to fantasize had burned through Biff's psyche leading him to falsely remember that Bill Oliver "once had said" that he would be willing to help him in any of his endeavors. This is not the case. Biff imagines all of this.
It is no surprise that, when Biff's fantasy takes him all the way to the office of Bill Oliver to request the help that Bill had supposedly offered, Bill Oliver does not even remember Biff and does not meet with him. This is the turning point in Biff's life: he now realizes that his life has been nothing but a compilation of Willy Loman's fantasies.
Back to Act 2, scene 5, the Loman men had planned to meet at a restaurant to celebrate the assured success of Biff's meeting with Oliver. At this point, Willy is already convinced that this will be a successful meeting. However, Biff has other plans in mind: he wants to confront Willy, for once and for all, about the false ideas that led him to such a ridiculous meeting in the first place.
Since Willy's mind is traveling from past to present, his hallucinations kept mixing him up between fantasy and reality. This made Biff mad and he obstinately continued to try to make his point. The discussion turned into a loud, public argument that left Happy as the mediator. Unfortunately, Happy was no good at this and his ideas of mediating were to pretend that everything was fine and to coerce Biff into leaving the restaurant with some girls who were presumably escorts that Happy met in the bar previous to the dinner. As a result, the Loman boys left their father at the restaurant, hallucinating, and left to his own devices. The only person to take care of Willy at that point was Stanley, the bartender, who was kind enough to help Willy find his way out.