In the play The Crucible, John Proctor claims that his wife cannot lie, and so when she is brought into the courtroom to confirm what is both a damning confession and accusation, the stakes are high. If Elizabeth confirms that Abigail and John had an affair, Abigail's power in the court will be at an end, and the witch trials will most likely trickle to a stop.
However, Elizabeth does not know that John Proctor has confessed in the courtroom to this affair. All she knows is that her husband's honor and moral goodness are being publicly questioned and denounced. In the Puritan tradition, adultery is considered a heinous sin and crime. If Elizabeth were to confirm that John and Abigail had had an affair, she would be exposing both of them to punishment, humiliation, and alienation by their community. She lies about the affair to protect her husband and his honor in the community.