Spee's authority comes from where he stood. As a Jesuit priest in the German prosecutions he was assigned to the condemned: he heard their last confessions and walked with them to the place of execution. A confession in that setting is made by someone with nothing left to gain by lying, and Spee wrote afterwards that he did not believe he had ever accompanied a guilty person.
That is not a theological claim and he was careful to keep it from becoming one. The Cautio Criminalis of 1631 does not argue that witches do not exist. It sets that question aside as one the book does not need, and attacks the procedure instead, question by question, in the dry manner of a legal treatise.
The core of it is a trap with no exit. Torture makes a person say what stops the torture, and what stops it is agreement. Once she has agreed there was a gathering she must say who else was there, so she names neighbours, and the neighbours are arrested. A defendant who denies is tortured for denying. One who confesses is executed. One who retracts is tortured again for retracting. Innocence has no available move.
Spee then makes the point that the judges could not answer: if the procedure would convict an innocent woman with the same certainty that it convicts a guilty one, then the convictions carry no information at all. Whatever the truth about witches, this court cannot find it.