How is Jimmy Porter portrayed as an "angry young man" in Look Back in Anger?
Jimmy is an angry young man because of personal tragedy and the social era. He also blames his personal tragedy on the social era. Jimmy's father died when Jimmy was ten years old from wounds inflicted while fighting in the Spanish Civil War, a popular thing for social activists to do in the cause of democracy. Jimmy stayed at the side of his father listening to him talk and talk during the six months that it took for his father to die. This leads to Jimmy's entrenched hatred for social ills, and one social ill that Jimmy feels particularly strongly about is that of social class division: the upper class in England versus the lower classes.
Jimmy lives in an era during which England is losing power as an Empire as more and more of its colonies are granted independence and upper classes resist the incursion of political changes, like the advent of a powerful labor party for working class people. It is a time also at which the Church of England is coming under political attack for being itself part of the upper classes (churches are meant to be for all) because the Church has vast and rich landholdings.
In addition, the era following World War II led to realistic fears for the annihilation of all classes through the threats of nuclear bomb attacks, resulting in Jimmy's own form of nihilism and existentialist despair:
If the big bang does come, and we all get killed off, it won't be in aid of the old-fashioned, grand design. It'll just be for the Brave New-noting-very-much-thank-you. About as pointless and inglorious as stepping in front of a bus.