Hey there! I'm doing Miller too for Mod C, first exam on tuesday, kinda procrastinating right now but I guess it's okay cause it's related hhahaha
anyway, basically Miller lived thru the McCarthy era, and he was inspired and also kinda disgusted at the way America was behaving at the time. he found out about the Salem witch trials, which is a historical and true event. he noticed that the two points in time, 1692 and the 1950s shared similar traits, and so he wrote the Crucible, as a kind of parable, allegory, or 'fairy tale' to subtly warn people of the way they were acting.
the way Americans were behaving in the 1950s was pretty crappy. everyone was paranoid and hysterical, and as a result the every day public gave up their rights of individualism and freedom to the government. the government, particularly senator mccarthy, actually took advantage of this fear as a way to control the public. they established the House UnAmerican Activities Committee (HUAC) which investigated any person who was deemed 'unAmerican'. huac basically accused the person, and investigated them thoroughly, making their private lives public, blacklisted them and generally took away their dignity, JUST BECAUSE THEY WERE ACCUSED. usually they were accused by someone else, either an enemy who was taking advantage of HUAC to destroy their reputation, or they were accused by another accused person who 'named names' so that they would be seen as innocent.
the reason why Miller was disappointed in his fellow americans was because they ALLOWED this to happen, when usually a person's moral compass would tell them that what was happening was wrong, and a perversion of justice.
in Salem, anyone could accuse anyone else of being a witch, and with no evidence except the accusation, the defendant would be convicted and hanged. the public didn't say or do anything then either, since they were a) too genuinely scared of witches, b) able to gain something eg land, from the person who would be hanged, c) anyone who said anything against the court was seen as guilty too.
so you see the similarities between the two? because millers play, with its dramatisation, makes the audience feel for the main characters, see the injustice, experience the pain of those affected by the trials, it also subtly makes the audience see their own cowardice as well.
mccarthy basically organised the whole thing, thats how he's connected to miller.
hope that helped