Strong inductive biases allow children to learn in fast and adaptable ways. Children use the mutual exclusivity (ME) bias to help disambiguate how words map to referents, assuming that if an object has one label then it does not need another. In this paper, we investigate whether or not vanilla neural architectures have an ME bias, demonstrating that they lack this learning assumption. Moreover, we show that their inductive biases are poorly matched to lifelong learning formulations of classification and translation. We demonstrate that there is a compelling case for designing task-general neural networks that learn through mutual exclusivity, which remains an open challenge.