What are judge danforth and the other authorities so resistant to believing the claim by john proctor that Abigail and the other girls are not telling the truth?

Judge Danforth and the other authorities are resistant to believing John Proctor's claim because they are heavily invested in the validity of the witch trials and the testimonies of the girls, which have been accepted as truth by the court. Acknowledging that the girls are lying would undermine their authority and the legitimacy of the trials, leading to a potential collapse of the societal order they are trying to uphold. Additionally, they are influenced by a fear of dissent and the possibility of admitting to their own mistakes, which could result in a loss of power and control.