Why does Elizabeth not tell the judge that Abigail is a whore in The Crucible?
She does not tell the judge this because she is worried about what her husband might have said.
In the part of the play that you are talking about, John Proctor is trying to tell the judge why there is bad blood between his wife and Abigail Williams. He is trying to show why Abigail would falsely accuse his wife of witchcraft. He tells the judge that Elizabeth threw Abigail out because he was having an affair with Abigail.
But Elizabeth doesn't know that John has admitted this. And she is too loyal to her husband. She doesn't want to tarnish his good name. So she says that that was not why she threw Abigail out. She says she just threw Abigail out because she thought her husband liked her, not because anything actually happened.
Elizabeth is a woman who believes in honesty and faith. She was told by her husband, John Proctor, that he had an affair with Abigail. After Abigail makes accusations against Elizabeth, Elizabeth still does not go forward to her accusers and state the truth about her husband's adulterous behavior.
Elizabeth is a good woman who can not hurt her husband. She also does not think that it is her place to tell the tale about her husband and Abigail. She tries to protect John but also to give John a chance to do what he has to do to make things right for him.
Another part of her does not think that the people will believe it even if she tells the truth. They are so wrapped up in their witch hunt that the truth is of little value.
By telling the judge about Abigail, she would have to tell about her husband.