Pedestrian motion prediction is a fundamental task for autonomous robots and vehicles to operate safely. In recent years many complex approaches based on neural networks have been proposed to address this problem. In this work we show that - surprisingly - a simple Constant Velocity Model can outperform even state-of-the-art neural models. This indicates that either neural networks are not able to make use of the additional information they are provided with, or that this information is not as relevant as commonly believed. Therefore, we analyze how neural networks process their input and how it impacts their predictions. Our analysis reveals pitfalls in training neural networks for pedestrian motion prediction and clarifies false assumptions about the problem itself. In particular, neural networks implicitly learn environmental priors that negatively impact their generalization capability, the motion history of pedestrians is irrelevant and interactions are too complex to predict. Our work shows how neural networks for pedestrian motion prediction can be thoroughly evaluated and our results indicate which research directions for neural motion prediction are promising in future.