This "argument" is a device of the sleepless Archfiend, the Adversary!
Mather was a devoted Anglican minister who completely believed in the existence of witches and demons and warned of the dangers posed to New England's "New Jerusalem" by the Archfiend, Satan himself.
The background makes it fun to pick your favorite archfiends, and easy to work up a ‘reason’ for the battle… I like the idea of exploring the politics of Hell.
Bands of angels and archangels follow the divine leader, while troops of demons and archfiends hasten after the evil lord.
Amelia Wilson's illustrated history of the Devil is a wonderful introduction to the myth of the Archfiend as he appears throughout history and across religions and cultures.
We are going to that castle over there, and striking a deal with the resident archfiend to make sure that they don't escape.