Why is John Proctor hesitant to expose 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.