Enhancing fairness in machine learning (ML) systems is increasingly important nowadays. While current research focuses on assistant tools for ML pipelines to promote fairness within them, we argue that: 1) The significance of properly defined fairness measures remains underestimated; and 2) Fairness research in ML should integrate societal considerations. The reasons include that detecting discrimination is critical due to the widespread deployment of ML systems and that human-AI feedback loops amplify biases, even when only small social and political biases persist.