There are several events which lead to Biff's ultimate discovery of the farce that is his life. They stem from the fantasies propelled by his father, Willy Loman. Since Willy thinks of himself as a successful salesperson living, or almost nearing, the American Dream, he naturally bestows upon his children the idea that they are just as successful, and that success is easily attained by simply being well-liked.
That alone is one of the worst paradigms of Biff's life. During his younger years, he would continuously use his talent in sports to belittle others and do self-serving behaviors, however wrong they might have been. As an adult, Biff still carries on with the same self-serving behaviors that were never corrected in him as a child: Lying, stealing compulsively, and creating fantasies in his head.
Growing up, Biff followed his father's strongest fantasy: That, one day, he would easily be a college football champion, that he would enter college, and that he would never have any troubles in life. Unfortunately for Biff he flunks Math in his Senior year of high school, loses his chance to go to college, and there is nothing anyone can do about it. When he goes to seek moral support from his father, by visiting him in Boston, he finds out that Willy has been leading a double life:He has a mistress whom he treats better than he does his own wife, Biff's mother.
This is a major event. Biff's image of his seemingly-almighty, protective, and loyal father goes straight to the ground. Along with it also went his own dreams, as they are an extension of Willy's fantasies. Slowly but surely, Biff reduces his potential to the minimum while still perpetuating the absurd hope (perhaps inherited from Willy) that he is close to "making it big" in business someday.
Yet, the final blow comes when even this idea comes crashing down. In hopes of solidifying his affirmation that he will create a partnership with his brother, Biff actually has the nerve to go ask a former boss, Bill Oliver, to loan him ten thousand dollars. All his life Biff has led himself to believe that he and Oliver were partners. In fact, Biff was insistent in that Oliver would welcome his request. But when Oliver did not even recognize Biff, he gets the final blow to his ego: He realizes that he has never been Oliver's partner, but just a shipping clerk in the company.
This is the event that directly prompts Biff to declare that all his life had been an illusion. He decides to tell his father, and Happy prevents it. Yet, Biff carries on and, during the restaurant scene, he openly declared that all that they believed in was a fake. As we know, Willy would not accept this. Yet Biff realizes finally that he needs to move away from the self-deception and open up to new horizons.