What is the real tragedy in Loman's family in Death of a Salesman?
The real tragedy with the Loman family in Death of a Salesman is a combination of lack of action, aptitude and attitude to attain the superbly high goals that the men of the family set for themselves.
Most people argue that the Lomans' true problem was their obscene ambition with attaining an American Dream that Willy built for them. The argument is also that such an American Dream was phony because it is based on shallow parameters, such as being "well-liked," attaining financial success with little work, and becoming popular. Although those are indeed the tenets of Willy's dream, calling the Lomans "ambitious" would be a problem.
First, ambitious people know what they want, stick with a plan, and fight until the end to get their goal. Additionally, truly ambitious people are not scared of defeat because they are willing to get up and try again by all means necessary. Third, people who really want a lot often already have a lot. Think of the quintessential "rich getting richer" paradigm, which presupposes that the ultimate ambitious person is that who has achieved a lot and still wants to achieve more.
Now, look at the Lomans. Here is Willy, dreaming of being like Dave Singleton, the salesman who could sell anything out of his hotel room. Biff wants to be "something" but he does not know what. Happy wants women, looks, popularity, and the position of his boss at his job. All three men are justifiably ambitious, but none of them has a single plan in place to carry on. They simply dream, hope, make limited attempts, and then find blame in one another, or something else, to diffuse their lack of action.
This being said, the true tragedy in the life of the Lomans can be summarized in one word: "indolence." Lack of movement, planning, changing, and moving toward a goal is their true problem. It is something that they have learned to live with, and they believe it to be the norm. It is also the reason why the three men are stunted compared to their peers, and why the Lomans may never really amount to anything as great as what they think.