This paper presents a process model of arguing with hypotheticals and uses it to explain examples of oral arguments before the U.S. Supreme Court that are like those employed in Socratic law teaching. The process model has been partially implemented in the LARGO (Legal ARgument Graph Observer) intelligent tutoring system. The program supports students in diagramming oral argument examples; its feedback on students' diagrammatic reconstructions of the examples enforces the expectations of the process model. The paper presents empirical evidence that features of the argument diagrams made with LARGO are correlated with independent measures of argumentation ability. The examples and empirical results support the model's explanatory and diagnostic utility.