Neural networks have proven to be effective at solving machine learning tasks but it is unclear whether they learn any relevant causal relationships, while their black-box nature makes it difficult for modellers to understand and debug them. We propose a novel method overcoming these issues by allowing a two-way interaction whereby neural-network-empowered machines can expose the underpinning learnt causal graphs and humans can contest the machines by modifying the causal graphs before re-injecting them into the machines. The learnt models are guaranteed to conform to the graphs and adhere to expert knowledge, some of which can also be given up-front. By building a window into the model behaviour and enabling knowledge injection, our method allows practitioners to debug networks based on the causal structure discovered from the data and underpinning the predictions. Experiments with real and synthetic tabular data show that our method improves predictive performance up to 2.4x while producing parsimonious networks, up to 7x smaller in the input layer, compared to SOTA regularised networks.