The witch craze to which you refer is presumably that which took place in Salem, Massachusetts between 1692- 1693. Prior to that witch craze, there was a longer one dating back to the late medieval period that ended with the advent of the Renaissance period in Europe (1300s to 1600s). Prior to this, religious sermons made to control people and their dependence on the church. These sermons proclaimed that the devil had the power to use humans directly to cause havoc, and fool others.
The most important reasons:
In Europe and America alike, the craze was first caused by the paranoia that resulted from the fear of being a victim of the devil. After the craze ended in Europe thanks to the advent of the Renaissance period, the colonists in America were still abiding by the Calvinist believes the devil being always around.
However, the second cause for the craze, in America, was resentment. The Salem colonists had family rivalries dating back to their time in England. They were living in dire circumstances, so they were frustrated, and tended to fight and bicker. To add to the mess the minister assigned to their parish was Reverend Paris, who was disliked by everyone. When the events of contorting and "possession" began to occur, the colonists used the devil as the scapegoat and began to blame one another for being possessed and deserving death.
Linda Caporael's study published in Science magazine in 1976 seems to be the most accepted theory of what took place in Salem: a fungus named ergot infected the wheat crops and partially poisoned people who showed the bodily behaviors thought to be part of a "possession". However, that aside, the desire that they had to tell on one another, to get each other in trouble, to accuse one another, and to label others as friends of the devil shows the anger and resentment that this community harbored to a dangerous degree. That combination of feelings ultimately caused the "witch craze" of Salem.
To shorten your answer, the second and third paragraph answer your question more concisely. The first and last paragraph were additional facts.
You can find more info on the Linda Caporael study in Science magazine.
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