Why is John Proctor hesitant to expose Abigail's lies?
On some level, Proctor is a bit leery of going after Abigail's hypocrisy because of the collateral damage on a social level that is going to be caused. I think that this is what motivates him to try to skirt around or dance around the issues of her motivation, and their relationship. At this level, I think this is when we see Proctor at not necessarily at his strongest. Yet, Proctor realizes the folly of this throughout the course of the play when he sees that the failure to stand up to Abigail's accusations ends up ripping apart the social fabric of the town and causes irreparable damage to people's lives and the way in which the town functions. It is at this moment when Proctor assumes a superhuman status from being quite normal and ordinary in his commitment to speaking the truth, regardless of the cost. It is something that ends up costing him his life, but is seen as a price worth paying if it will stop the spread of evil. This level of moral ascendancy is not present at the start of the drama, and could be a major reason why we see Proctor as displaying ambivalence towards Abigail's lies.
John Proctor is having quite the dilemma. Whether in Act I or Act III, Proctor is reluctant to expose Abigail because if he does, she has quite a bit that she can say about him. You know how kids are, if one tries to tell on another, the second child will tell some other detail on the first. This is the same situation. If John reveals Abby's lies, Abby can reveal a secret that is much more shameful in a Puritan society: their adulterous affair. Should Abby bring this detail to the surface, not only would John Proctor's reputation be stained, but under the current circumstances he would likely be named as one who was working with the Devil.