In "The Black Walnut Tree" by Mary Oliver, a daughter and her mother are discussing whether they should sell the black walnut tree. The situation is not one of an argument in which either of them is trying to persuade a third party, nor is it a debate in the real sense of two people each with opposing opinions trying to convince each other of something. Instead, mother and daughter are trying to talk with each other and explore their options and feelings together. Thus classical rhetorical analysis is really not an entirely appropriate tool for thinking through the poem.
There are many practical reasons for selling the tree. First, it would pay off the mortgage. Second, the tree is so large it may suffer storm damage. The tree roots could injure the cellar and drains.
On the other hand, the women both feel a strong emotional connection to the tree. It represents their connection with their ancestors and ethnic heritage, and without it the yard would feel empty. Eventually, their emotional attachment to the tree and what it signifies is more important to them than the financial value of the tree or the other practical reasons for removing it.