Self-explainable deep neural networks are a recent class of models that can
output ante-hoc local explanations that are faithful to the model's reasoning,
and as such represent a step forward toward filling the gap between
expressiveness and interpretability. Self-explainable graph neural networks
(GNNs) aim at achieving the same in the context of graph data. This begs the
question: do these models fulfill their implicit guarantees in terms of
faithfulness? In this extended abstract, we analyze the faithfulness of several
self-explainable GNNs using different measures of faithfulness, identify
several limitations -- both in the models themselves and in the evaluation
metrics -- and outline possible ways forward