The power of human language and thought arises from systematic compositionality—the algebraic ability to understand and produce novel combinations from known components. Fodor and Pylyshyn1 famously argued that artificial neural networks lack this capacity and are therefore not viable models of the mind. Neural networks have advanced considerably in the years since, yet the systematicity challenge persists. Here we successfully address Fodor and Pylyshyn’s challenge by providing evidence that neural networks can achieve human-like systematicity when optimized for their compositional skills. To do so, we introduce the meta-learning for compositionality (MLC) approach for guiding training through a dynamic stream of compositional tasks. To compare humans and machines, we conducted human behavioural experiments using an instruction learning paradigm. After considering seven different models, we found that, in contrast to perfectly systematic but rigid probabilistic symbolic models, and perfectly flexible but unsystematic neural networks, only MLC achieves both the systematicity and flexibility needed for human-like generalization. MLC also advances the compositional skills of machine learning systems in several systematic generalization benchmarks. Our results show how a standard neural network architecture, optimized for its compositional skills, can mimic human systematic generalization in a head-to-head comparison. The meta-learning for compositionality approach achieves the systematicity and flexibility needed for human-like generalization.