The most obvious reason Arthur Miller wrote The Crucible (or anything else, really) is because he had a story to tell. Without that, he would not have been inspired to write. It is true, however, that what inspired him to write this particular story is quite personal.
As a Jewish man, Miller was a political advocate against the inequalities of race in America, and he was vocal in his support of labor and the unions. Because he was such an outspoken critic in these two areas, he was a prime target for Senator Joseph McCarthy and others who were on a mission to rid the country of Communism.
Miller was called before the House Committee on Un-American Activities because of his connections to these issues but refused to condemn any of his friends. This experience, a rather blind and sweeping condemnation of anything even remotely connected to Communism without sufficient (or any) evidence, is what prompted him to write about the Salem Witch trials.
In a later interview, Miller said the following:
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