Death of a Salesman involves Willy Loman in many conflicts. He is in conflict with society as well as in his own family and most importantly himself. Willy is trying to provide for his family and become economically mobile. He wishes the same life that he dreams of for his sons, especially Biff. Biff will become the icon for Willy's success during the play.
Biff is constantly arguing with his father because he sees what Willy cannot. Biff sees that Willy's life has not fulfilled his dreams and the life that Willy wants for Biff will not fulfill Biff's dreams either. Willy wants to live the American Dream and be successful and get promoted and have successful children. He is constantly lying to himself to make it seem that the situation is as he thinks it should be. He is always thinking of the past because those days had much better prospects. Biff, however, sees the truth in his life and wants Willy to see it too. Biff's efforts to make Willy see what he really is come off as "spite" and instead of being Biff's downfall as Willy says, they end up being Willy's downfall when Biff is finally successful in making Willy see what he has amounted too. .
Biff wants to go out on his own and do as he pleases. He desires to be out in the open and work with his hands. He dreams of being his own boss, partly because of Willy's encouraging him to strive for that as a teenager. Biff subconsciously sabotages every corporate job he has by stealing because he is not the boss. Willy cannot stand to see Biff fail like he has and cannot believe that he is happy working outdoors on farms. Biff's desired life is not part of the American Dream. .
Willy not only lies to himself, he lies to Biff. He tells that who you know and whether they like you is what determines success. This is untrue and causes Biff not to work hard in school because he is well liked. Willy also lies to Biff about The Woman and who she is after it is clear he has been caught cheating.