Why did Arthur Miller write The Crucible?

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:

It would probably never have occurred to me to write a play about the Salem witch trials of 1692 had I not seen some astonishing correspondences with that calamity in the America of the late 40s and early 50s. My basic need was to respond to a phenomenon which, with only small exaggeration, one could say paralysed a whole generation and in a short time dried up the habits of trust and toleration in public discourse.

However, the more he began to study the tragic events in Salem, the more he understood that McCarthy's hunt for Communists was nothing compared to the fanaticism which reigned in Salem in the 1690s.

In time to come, the notion of equating the red-hunt with the witch-hunt would be condemned as a deception. There were communists and there never were witches. The deeper I moved into the 1690s, the further away drifted the America of the 50s, and, rather than the appeal of analogy, I found something different to draw my curiosity and excitement.

Anyone standing up in the Salem of 1692 and denying that witches existed would have faced immediate arrest, the hardest interrogation and possibly the rope. Every authority not only confirmed the existence of witches but never questioned the necessity of executing them. It became obvious that to dismiss witchcraft was to forgo any understanding of how it came to pass that tens of thousands had been murdered as witches in Europe. To dismiss any relation between that episode and the hunt for subversives was to shut down an insight into not only the similar emotions but also the identical practices of both officials and victims.

In his note about the historical accuracy of the play, Miller writes:

I believe that the reader will discover here the essential nature of one of the strangest and most awful chapters in human history.

Though his interest in the comparisons between the trials and McCarthyism began with his own experience, it was the horrific nature of the trials themselves which motivated Miller to write The Crucible. 

Here's a great interview with Arthur Miller about why he wrote the Crucible and its parallels to modern life: