It is not clear to me that Reverend Hale really does have any special insight into witchcraft even though he has been called to Salem especially to find out if there is any witchcraft happening there.
What we know of Hale's insight comes from Miller's narrative just before Hale is introduced to the action. We are told that Hale has studied witchcraft and the supernatural a great deal. So he at least has book knowledge about the subject. However, he has never actually dealt with an example of witchcraft because he has only ever investigated one case. In that case, he decided the suspect was not a witch.
From what we see in Hale's early dealings with the Proctors, he believes that someone might be a witch if they don't go to church enough or if they don't know all the commandments.
Later on, Hale realizes that there is no witchcraft in Salem, but he is not strong enough to do anything to stop the trials.
In the play "The Crucible" Reverend Hale is brought into the town by Reverend Parris. The Reverend wants Hale to examine his daughter Betty. The only thing that gives one to think that Reverend Hale has any expertise in witchcraft is that he brings books with him on the topic. Mostly Hale is a person who prides himself in his knowledge which enables him to present himself as the expert in the field.
On page 39 of the book (Penguin Plays), Hale refers to his books in the following manner:
"In these books the Devil stands stripped of all his brute disguises."(39)
The Reverand speaks in such a manner as to present himself knowledgeable about the devil's ways.