What conflicts did Willy Loman face with society in Death of a Salesman by Arthur Miller?

One of the major conflicts that Willy Loman faces in Death of a Salesman is his conflict with society, which arguably springs from his own conflict with himself. As his issues with himself develop, so too do his conflicts with society as a whole. For example, he feels bitter about the fact that as he ages, he has more difficulty making sales that would have once been easy for him as a younger man. This results in a lot of anger and philosophical questioning of the meaning of this betrayal and judgment by a society that once celebrated him. He believes that there is some sort of "trick" or key to success for selling, and he is on a constant search to find it, but to no avail.

Willy's main issue is actually that he believes people are judging him on his clothes, his weight, and his looks, when really they are just looking for a knowledgeable salesman, or no salesman at all, as times are changing and there is little need. While he is blaming his lack of success on his physical traits, he is coming across as delusional and strange to others; he has a hard time seeing this for himself, however.

Willy wants to stay in New York to sell, because he thinks that he will do well there, but his boss has other ideas. This causes Willy to believe that he is being sold out and "thrown away" by a company that he has worked for for 34 years. He believed that he was living the American dream, and now he believes that he is being treated carelessly, with no more regard than an orange peel that is being thrown away. On page 82, he exclaims "a man is not a piece of fruit!" 

In this case, he is referring to the way in which society "eats" the best part of the man, which would be his youth and his good years of work and service, and then tosses the rest out when there is no longer a use for him. This, essentially, is what happens to him in the play.  A man's worth in society is measured by two things: his skills and his ability to generate income. Well, at the end of the play, it turns out Willy has achieved neither of these things and so has been unsuccessful in life. At his funeral, the only people who attend are his family, Charley, and Bernard.