Rev. Parris refuses to consider witchcraft the reason for Betty's illness is simple: as the town preacher, he does not want his holiness cast into doubt as a result of his daughter being a witch. Add to this his already poor reputation among many of the townsfolk, including John Proctor, and he would do anything to make sure he would keep his job.
Historically, the place of the preacher in these Puritan towns was always tenuous. This is the case in this part of the novel.
In the overture, Arthur Miller writes about Rev. Parris's character: "He believed he was being persecuted wherever he went, despite his best efforts to win people and God to his side."
This characteristic is clear in the opening scene when his help, Susanna, suggests that he "might look to unnatural things for the cause of [Betty's illness]." To this, Rev. Parris responds forcefully saying that Rev. Hale was on his way to confirm this. He says, "Let him look to medicine and put out all thought of unnatural causes here. There be none."
Proctor criticizes Parris for demanding the deed to his house while no other ministers asked for it before. In addition, Proctor does not like Parris's preaching style, particularly his sermons about burning in hell. When Parris demands obedience to the church from Proctor and threatens a burning hell, Proctor says, "Can you speak one minute without we land in hell again?"
In Salem, Proctor is influential. When the sickness breaks out many people in the village turn to him for direction. These segments of this society threaten Parris's job security, which is why he can't have his daughter afflicted from some type of witchcraft.