In an inductor-switch circuit, closing the switch creates a scenario where currents I1 and I2 may appear independent due to the zero voltage across the short circuit. However, the discussion highlights that the two currents are not entirely independent because they flow through the same circuit elements, which creates a dependency. The presence of shared components means that changes in one current can affect the other. This interconnectedness raises questions about the nature of current flow and dependency in circuit analysis. Ultimately, while the currents may seem independent at first glance, their interaction through shared elements indicates a level of dependence.