Christine Caldwell Ames sets this history in the context of medieval beliefs about heresy.
Context is very important for understanding the medieval inquisition: understandings of the Body of Christ; what it meant to be Christians in community; what it meant to have wrong belief; the stakes of that wrong belief. And I think, yes, even though very often we think of heresy as an issue of individual wrong belief, in the Middle Ages people thought that this individual wrong belief could potentially be contagious – that a neighbour, a friend, a spouse might inherit or catch that wrong belief. And so this absolutely is one of the most important things to understand about how people conceived of medieval inquisitions.
The other thing to keep in mind about medieval inquisitions and the context in which they arose in medieval Europe is the question of God simply not wanting Christians to err. That again, this kind of consequence for wrong belief – that he had issued to Christians, via the revelation of Christ, a correct belief, a set of correct beliefs that, yes, had been worked on and nurtured throughout centuries in the church, but that nevertheless, again, to be wrong was to be cataclysmically wrong, and it had consequences, eternal consequences, if it was not corrected.