This is a long answer, but there is a lot going on in 1692 that contributed to the trials. Recent history of the trials focuses on the influence of the Maine frontier. Throughout the 17th century, the colonists and the Indians were constantly fighting. In 1675-76 King Philip's War and in 1688-97 (overlapping the trials) King William's War brought war paranoia across Massachusetts Bay Colony and New England. Much of the testimony of the Salem Witch Trials referenced Indians and fighting. The Puritans believed the Indians were minions of the Devil, so the war felt like an attack on Puritanism. Roughly 1/3 of the people involved in the Salem Witch Trials had a direct tie to the frontier (by fighting in the war, having a relative who did, or being a refugee from Maine) which gave this threat a very real tie to many accusers and accused. Mary Beth Norton's book In the Devil's Snare was the first to extensively cover these ties. Emerson W. Baker's book A Storm of Witchcraft also covers this a lot.

Why it spread in the manner it did is from the judges. In Connecticut, there were accusations made as well (unrelated to Salem), but the judges stopped the spread. In Massachusetts, the politics of the day impacted the judges. In May 1692, Gov. William Phips set up a court to hear all the accusations. 8 of the 9 judges on the court were related by family marriages. This was common for the political elite. These 9 judges were the political leaders, military leaders, and excessively wealthy. Politics in Massachusetts were in flux at the time. In 1684, the colony's charter was revoked by England since the colony began to get too autonomous. In 1685, King James II instated the Anglican Sir Edmund Andros to lead the Dominion of New England, a super colony of all the New England colonies together as one. In 1689, a revolt against Andros restored New England to its previous state, but the charter was not yet restored until Sir William Phips was appointed governor and arrived in May 1692. The judges were also military leaders. They commanded troops on the frontier, decided where to send soldiers, and observed training. This tied into their economic position. Many of the judges, in particular Hathorne and Corwin, owned land on the frontier. They speculated land and owned saw mills in areas continually raided by Indians. Their property was being razed resulting in huge financial losses. In modern numbers, these were millions of dollars of losses. In a lecture I attended by Emerson Baker, he referred to the judges as the 1% of the 17th century if that helps to illustrate their standing.

So the judges were leading a politically unstable colony, commanding a disastrous war with Indians, and faced extreme financial loss. If anyone were to blame for the political and military situation of the colony, the judges were the ones to blame. However, Puritans believed Satan and his witches could bring this sort of upheaval to the colony. If the judges blamed witches (and they probably did believe most if not all of these suspects were witches), it took the blame away from the judges. No one put the accusations in check so it allowed the accusations to continue and eventually spiral out of control.

Richard Latner wrote an article titled "The Long and Short of Salem Witchcraft" which considers the chronology of accusations. Given that nearly every town in the region had some accusation, the timeline matters a lot when studying the trials. Latner argues that the general trend is each town had its own small witch hunt. Collectively, these small witch hunts are known as the Salem Witch Trials. I would disagree with him in part. I am currently writing my undergrad thesis where I challenge part of Latner's work. Rather than many small witch hunts, I would say there are 2 events. The accusations either center around local politics or the Indian wars. These two themes of accusations are what we call the Salem Witch Trials.

Your comment on the archaic and irrational nature of the trials is a common thought, but a lot of Salem historians would ask, is it really archaic? Emerson Baker ends his book suggesting if you switch the word 'witch' and 'terrorist,' you could start to understand the fear the Puritans felt. The Salem Witch Museum ends with a wall comparing other scapegoats in history,- Jews in the Holocaust, Japanese during internment, and gays during the AIDS epidemic. So how irrational is a belief in witches? Many historians would say we've only changed the name.