What is Arthur Miller trying to say about the "American Dream" in Death of a Salesman?

Death of a Salesman is centered around one man trying to reach the American dream and taking his family along for the ride. The Loman's lives from beginning to end is a troubling story based on trying to become successful, or at least happy. Throughout their lives they encounter many problems and the end result is a tragic death caused by stupidity and the need to succeed. During his life Willy Loman caused his wife great pain by living a life not realizing what he could and couldn't do. Linda lived sad and pathetic days supporting Willy's unreachable goals. Being brought up in this world caused his children to lose their identity and put their futures in jeopardy. You can check out the rest of this excerpt at the source-link below.

Here is another excerpt that describes Willy's imposition of the "American Dream" on his son Biff. To the protagonist of Death of a Salesman, the American Dream is the ability to become prosperous by mere charisma. Willy believes that personality, not hard work and innovation, is the key to success. Time and again, he wants to make sure his boys are well-liked and popular. For example, when his son Biff confesses to making fun of his math teacher’s lisp, Willy is more concerned with how Biff’s classmates react:

BIFF: I Crossed my eyes and talked with a lithp.

WILLY: (Laughing.) You did? The kids like it?

BIFF: They nearly died laughing!

Of course, Willy’s version of the American Dream never pans out. Despite his son’s popularity in high school, Biff grows up to be a drifter and a ranch-hand. Willy’s own career falters as his sales ability flat-lines. When he tries to use “personality” to ask his boss for a raise, he gets fired instead.

The original title of this play was 'Inside a Man's Head,' a much more leading title as to theme than the final product. Willy and Linda are content in their lives and their marriage; their one overwhelming desire and focus is to own their own home by paying off their mortgage. Ownership, a huge part of the American dream.

Willy Loman's character is broken by an unfeeling profession. It's often thought that what seems to be Miller's criticism of the American Dream stems from his socialist views. Willy believes that success hinges on a charismatic personality, that if you're popular and well liked, you can attain anything you wish. This is his preferred work ethic and the one he passes down to his children.

Willy's parental teachings don't pan out the way he'd believed. His son grows up to be a drifter, and he himself is fired from his job because his performance in no way lives up to his perceived ability to charm.

In the end, we see Willy working around the house, building a garage, using his hands and being happy. His American Dream became nothing more than a nightmare, and the things that made him happy were really the dream.