Computational models are powerful tools--too powerful, according to some. We argue that the idea that models can "do anything" is wrong, and we describe how their failures have been informative. We present new work showing surprising diversity in the effects of feedback on children's task-switching, such that some children perseverate despite this feedback, other children switch as instructed, and yet others play an "opposites" game without truly switching to the newly instructed task. We present simulations that demonstrate the failure of an otherwise-successful neural network model to capture this failure. Simulating this pattern motivates the inclusion of updating mechanisms that make contact with a growing literature on frontostriatal function, despite their absence in theories of the development of cognitive flexibility. We argue from this and other examples that computational models are more constrained than is typically acknowledged and that their resulting failures can be theoretically illuminating. (Contains 5 figures.)