There are remarkable behavioral, neural, and genetic similarities between song learning in songbirds and speech acquisition in human infants. Previously, we have argued that this parallel cannot be extended to the level of sentence syntax. Although birdsong can indeed have a complex structure, it lacks the combinatorial complexity of human language syntax. Recently, this conclusion has been challenged by a report purporting to show that songbirds can learn so-called context-free syntactic rules and then use them to discriminate particular syllable patterns. Here, we demonstrate that the design of this study is inadequate to draw such a conclusion, and offer alternative explanations for the experimental results that do not require the acquisition and use of context-free grammar rules or a grammar of any kind, only the simpler hypothesis of acoustic similarity matching. We conclude that the evolution of vocal learning involves both neural homologies and behavioral convergence, and that human language reflects a unique cognitive capacity.