Why would Elizabeth lie about the affair between Abigail and John Proctor in The Crucible by Arthur Miller?

In Arthur Miller's play "The Crucible," Elizabeth Proctor does not lie about the affair between Abigail Williams and John Proctor. In fact, she is the only one who knows about the affair and keeps it a secret to protect her husband. It is Abigail who lies about the affair to accuse Elizabeth of witchcraft and get rid of her as a rival for John Proctor's affections.