Recent datasets expose the lack of the systematic generalization ability in standard sequence-to-sequence models. In this work, we analyze this behavior of seq2seq models and identify two contributing factors: a lack of mutual exclusivity bias (one target sequence can only be mapped to one source sequence), and the tendency to memorize whole examples rather than separating structures from contents. We propose two techniques to address these two issues respectively: Mutual Exclusivity Training that prevents the model from producing seen generations when facing novel examples via an unlikelihood-based loss, and prim2primX data augmentation that automatically diversifies the arguments of every syntactic function to prevent memorizing and provide a compositional inductive bias without exposing test-set data. Combining these two techniques, we show substantial empirical improvements using standard sequence-to-sequence models (LSTMs and Transformers) on two widely-used compositionality datasets: SCAN and COGS. Finally, we provide analysis characterizing the improvements as well as the remaining challenges, and provide detailed ablations of our method.