Mrs. Phelps cries when Montag reads the poem because she hears emotion in his words.
One of the points made by society in removing all literature is that literature is harmful. When Montag reads the poem, he read “in a low, stumbling voice that grew firmer as he progressed from line to line” (Part Two). However, there is power in poetry. Their society is not wrong about that. Mrs. Phelps is upset. She is carried away by the emotion of the poem because she has never heard a poem read before. She begins crying, and she is not sure why. When the others ask, she responds that the poem is bad, and that’s why she was crying.
"You see? I knew it, that's what I wanted to prove! I knew it would happen! I've always said, poetry and tears, poetry and suicide and crying and awful feelings, poetry and sickness; all that mush! Now I've had it proved to me. …" (Part Two)
When she describes Montag as “nasty” and says that he has “proved” that poetry is terrible, she is just reacting the way society has told her to react. She has been conditioned to believe that literature is bad, emotion is bad, and in fact all feeling is bad. She is experiencing is emotion, and it is a foreign experience for her. She does not know how to react. She responds by attacking Montag, and literature in general.
Mrs. Bowles buys right in, asking why anyone would want to hurt people with things like this. They have both missed the point. Feelings are part of humanity. By denying our feelings, we deny our humanity and create a soulless society—which is exactly why no one talks to each other and teenagers joyride through the streets running over people for fun. Mildred suggests they turn on the television and watch the ‘family,’ because the shows are specifically designed to not create any emotions in people.
The poetry reading and the strong reaction it gets are an example of what happens when you lock away all of the emotions in a society. Emotions are part of life, and part of being human. As humans, when we try to ignore these emotions we only create an artificiality which is not healthy. This is why the ladies reacted so strongly to the poetry reading, and it is exactly why as a society we created the arts, and why we need them as a form of self-expression and communication.