Mr. (Carl) Rogers' Neighborhood

Like James Kastely, I too think that argument is problematic. I agree that an argument presented as a written text, distributed to an audience that neither knows the writer nor can have him or her present to discuss his or her position is relatively powerless compared to a spoken argument, present in a face-to-face conversation. Rogerian argument seeks to empower the written argument by bringing the writer and the reader closer together, to do away with the conflict between the writer and reader.
This is the goal of some of the assignments I have seen students bring into the writing lab. The instructor asks the student to begin by finding a written argument (a newspaper editorial, a piece of literary criticism, etc.) and summarize it. Then, the student must write an essay arguing how his or her experience (life experience in the case of the editorial, experience with the primary text in the case of the literary criticism) contradicts, complicates, or contributes to the original argument. Assuming that the student’s audience is familiar with the original argument (perhaps even convinced by it), the student is presenting a Rogerian argument by presenting an alternative viewpoint without threatening the reader’s stable image.
For my second assignment, I would consider asking students to engage in this approach, calling for them to make powerful arguments by considering Rogerian rhetorical theory. Here, I already ask students to find an argumentative text (allowing them to choose not just editorials and literary criticism but also movies and books). Instead of asking them to simply analyze the argument, I could ask them to summarize it, opening the lines of communication between writer and reader, then ask them to make some kind of contribution to it. My only hesitation is that for students to argue how their experience contradicts, complicates, or contributes to the original argument, they might have to do some more research so that they can have ample experience with that issue.