Why are Danforth, Hathorne, etc. so resistant to believing the claim that Abigail and the other girls are lying?
Miller's construction of the legal system of Salem is an interesting one. On one level, Miller suggests that part of the reason why men like Danforth and Hathorne are hesitant to view the girls as liars is because to do so would contradict their belief of what it means to be a "good Christian." Miller establishes that Salem is driven feverishly to embrace a construct of spirituality in dogmatic terms. Religious devotion in Salem is blindly accepted without much in way of reflection or proposal of alternate construction. Power and authority speak to what it means to be a "good Christian" and everyone else follows. Danforth speaks to this in his own testimony of what he has witnessed in presiding over the trials:
I tell you straight, Mister-I have seen marvels in this court. I have seen people choked before my eyes by spirits; I have seen them stuck by pins and slashed by daggers. I have until this moment not the slightest reason to suspect that the children may be deceiving me. Do you understand my meaning?
Leaders like Hathorne and Danforth are shown to sincerely believe in the court's cause. They believe that their work is reflective of a "good Christian." To accept that the girls were lying is a repudiation of that, challenging their dogmatic notion of spirituality. To accept that the girls are lying and that the premise of witches in Salem is false goes against their perception of what it means to be a "good Christian." The loss of such a view of faith is unfathomable for men like Danforth and Hathorne as well as majority of Salemites.
The other reason why men like Danforth and Hathorne cannot accept that the girls are lying is because of power. Miller develops the Salem legal system as one predicated upon the notions of power. Hathorne and Danforth have gained great power and prestige as a result of their presiding over the trials. They are known. They are respected. They have control over others' lives in Salem. Miller shows how power is seductive, its trappings so alluring that even the truth can be rejected in the name of control and consolidation of greater power. If the court accepts that the girls are lying, the trials are over and their power goes away. Miller shows that there were people in Salem who directly benefited from the trials, and some of them wore judicial robes.
At first, Danforth, Hathorne and the other authorities may have truly believed the girls were telling the truth. For this reason, these judicial authorities could not possibly admit that they may have been mistaken. To do so would have ruined their reputations. During this time, reputation was quite important. Even Elizabeth Proctor is willing to lie to protect her husband's reputation. Ultimately, John Proctor chooses to give up his life to protect his name. The irony is that Proctor dies to save his name while the judges allowed his death to protect their reputations.
No doubt, Danforth and the other authorities began to suspect that they may have been duped by Abigail and the other girls, especially after learning the girls danced naked in the woods. However, to admit an error in judgment would have been an end to their prestigious careers. Danforth and Hathorne have been enjoying their power and control. They take pride in the honor that the community has showered upon them. If Danforth and Hathorne admit that they have been deceived by children, they would become a laughing stock. Over all, Danforth, Hathorne and the other authorities are the real danger in Salem. They would allow innocent people to die to save their judicial reputations.