Reinforcement learning (RL) offers a compelling account of how agents learn complex behaviors by trial and error, yet RL is predicated on the existence of a reward function provided by the agent's environment. By contrast, many skills are learned without external guidance, posing a challenge to RL's ability to account for self-directed learning. For instance, juvenile male zebra finches first memorize and then train themselves to reproduce the song of an adult male tutor through extensive practice. This process is believed to be guided by an internally computed assessment of performance quality, though the mechanism and development of this signal remain unknown. Here, we propose that, contrary to prevailing assumptions, tutor song memorization and performance assessment are subserved by the same neural circuit, one trained to predictively cancel tutor song. To test this hypothesis, we built models of a local forebrain circuit that learns to use contextual input from premotor regions to cancel tutor song auditory input via plasticity at different synaptic loci. We found that, after learning, excitatory projection neurons in these circuits exhibited population error codes signaling mismatches between the tutor song memory and birds' own performance, and these signals best matched experimental data when networks were trained with anti-Hebbian plasticity in the recurrent pathway through inhibitory interneurons. We also found that model learning proceeds in two stages, with an initial phase of sharpening error sensitivity followed by a fine-tuning period in which error responses to the tutor song are minimized. Finally, we showed that the error signal produced by this model can train a simple RL agent to replicate the spectrograms of adult bird songs. Together, our results suggest that purely local learning via predictive cancellation suffices for bootstrapping error signals capable of guiding self-directed learning of natural behaviors.