Your Justice Would Freeze Beer
What is meant by the line in 'The Crucible' where John says to Elizabeth just after an argument, "Your justice would freeze beer?"
John Proctor feels that his wife, Elizabeth, has still not forgiven him for his infidelity in their marriage, despite the fact that his affair with Abigail Williams ended some seven months ago. Elizabeth is suspicious of John after he reveals that he was "for a moment alone" with the girl in town when he had made it sound like he spoke to her with other people present. Elizabeth tells John that he feels judged because he continues to judge himself for his sins. She says to him "the magistrate sits in your heart that judges you." However, he does not accept this, and her statement elicits the response from him that you quote in your question.
John's statement that Elizabeth's "justice would freeze beer" means that her justice contains no warmth; it is cold. This is because alcohol doesn't freeze at the same temperature as water. Water freezes at 32 degrees Fahrenheit, but pure alcohol doesn't freeze until it hits -173 Fahrenheit. Now, beer is not pure alcohol, so it will freeze (being mostly water), but it takes colder temperatures to freeze beer than it does water, and beer won't freeze as solidly as water does. Therefore, John implies that Elizabeth and her justice are very cold (figuratively): he means that she is somewhat without feeling and merciless. It is most decidedly not a compliment.
The author is using a colorful figure of speech to express John Proctor's belief that his wife Elizabeth's practice of justice is cold and harsh; lacking mercy and forgiveness.
John Proctor has cheated on Elizabeth, but although he has confessed and repented, she cannot let it go. She says she has forgiven and forgotten, but still acts with bitterness and suspicion. Elizabeth says to John, "I do not judge you...I never thought you but a good man", yet her cool distantness towards him says otherwise, and he responds, "your justice would freeze beer!"
John does not feel that Elizabeth has forgiven him. In answer to her verbal protests to the contrary, he elaborates in explanation,
"Spare me! You forget nothin' and forgive nothin'. Learn charity, woman. I have gone tiptoe in this house...I have not moved from there to there without I think to please you, and still an everlasting funeral marches round your heart. I cannot speak but I am doubted, every moment judged for lies, as though I come into a court when I come into this house" (Act II, Scene 1).
John believes Elizabeth is somewhat heartless and unforgiving because she judges him for his past indiscretions. However, he feels she led him to this course of action through her behavior toward him. Elizabeth, because of her own low view of herself, judges Proctor more out of displeasure with her own failings as a wife than any misconduct on John's part. The church's influence, too, has much to do with this, but as the play goes on, we learn that Elizabeth's own self-loathing and feelings of inadequacies prompt her to be very cold toward John.