In the overture prior to Act One, Parris is described as one who "cut a villainous path" in history. "In meeting, he felt insulted if someone rose to shut the door without first asking his permission." Parris is insecure and feels threatened when anyone questions his authority.
When Proctor is introduced in Act One, he had a "sharp and biting way with hypocrites" and that he was "not easily led." That being said, an insecure man like Parris is not likely to get along with a man like Proctor who is more than willing to call him on his selfish grasp on his religious authority. Proctor is quite clear that he does not care for Parris as a preacher:
I have trouble enough without I come five mile to hear him preach only hellfire and bloody damnation. Take it to heart, Mr. Parris. There are many others who stay away from church these days because you hardly ever mention God any more.
Parris claims that Proctor is a part of some faction against him. Proctor, totally annoyed with Parris self-righteousness and claims to authority, says that if such a faction exists, he would like to join it. Parris does fear and distrust Proctor because he sees Proctor as an enemy and a threat. This is because Proctor has always been critical of Parris's selfish behavior.