How are visuomotor mismatch responses in primary visual cortex embedded into cortical processing? We here show that mismatch responses can be understood as the result of a cooperation of motor and visual areas to jointly explain optic flow. This cooperation requires that optic flow is not explained redundantly by both areas, meaning that optic flow inputs to V1 that are predictable from motor neurons should be canceled (i.e., explained away). As a result, neurons in V1 represent only external causes of optic flow, which could allow the animal to easily detect movements that are independent of its own locomotion. We implement the proposed model in a spiking neural network, where coding errors are computed in dendrites and synaptic weights are learned with voltage-dependent plasticity rules. We find that both positive and negative mismatch responses arise, providing an alternative to the prevailing idea that visuomotor mismatch responses are linked to dedicated neurons for error computation. These results also provide a new perspective on several other recent observations of cross-modal neural interactions in cortex.