The new old story
There is an irony in this punchy and extremely powerful essay where Plaskow remembers a story that is archetypal and extremely well-known. It might be the central story of Western civilization, and yet, Plaskow flips it on its head. This artistic irony is a helpful way of analyzing the essential irony of the divine story in the first place; throughout Plaskow's narrative, God talks to Adam in a way that seems encouraging and compassionate, but he is clearly teaching Adam a difficult lesson in humility. The irony is this: Why would a supreme being make life so dramatic and painful? Plaskow predicates human history not on marriage, as classical religion, but on divorce.
The demon irony
Lilith and Adam are the same. Yes, they are foils, but that is precisely the purpose of their foil. Lilith is a foil for Adam because they are equal in every single way except one, and Adam uses that one indifference to disparage Lilith, even though she is a primordial wife to him. He says she is a demon, and many historical Jewish writers have conceived Lilith as the primordial demoness, but that is ironic, because this story remembers her origin as a pure manifestation of the divine. She is the ironic hero, much like Paradise Lost takes Lucifer as its protagonist for portions of the poetry.
Eve's irony
Eve experiences dramatic irony because she is unaware of Lilith's true nature. That is a symbolic way of saying she has not discovered the feminine spirit which is pridefully equivalent to masculine authority. To be more specific, Eve is ironic because she does not know what feminism will reveal to her. By climbing a wall to discover something new, she realizes that Lilith is not what Adam has told her. Lilith becomes her best friend. By the end of their first conversation, they have held each other and wept, and also laughed hysterically.
Adam's moral irony
Adam is an ironic character because he allegedly has free will, as the story famously indicates, but Adam is also compelled by his design and character. He is morally ironic because all of the physical aspects of his character lead him naturally toward misogyny, so that when confronted with his arrogance and evil, he is confused and plays the victim. He ends up the same way many misogynists end up; alone with God, thinking through the past and wondering where things will go in the future.
God's ironic character
God is ironic in this narrative essay because the creator of the universe also belongs within that universe as an agent and character. That would be like if an author wrote a novel and included himself as a character. That becomes more ironic the more God's character is amplified. As the master architect of all reality and conscious experience, why would God be surprised or frustrated, as he appears in the story? The narrative introduces this irony to suggest that God is playing. He is playing a part, and perhaps he is playing with reality for interest and fun.