The evaluation of fairness in machine learning systems has become a central concern in high-stakes applications, including biometric recognition, healthcare decision-making, and automated risk assessment. Existing approaches typically rely on a small number of fairness metrics to assess model behaviour across group partitions, implicitly assuming that these metrics provide consistent and reliable conclusions. However, different fairness metrics capture distinct statistical properties of model performance and may therefore produce conflicting assessments when applied to the same system. In this work, we investigate the consistency of fairness evaluation by conducting a systematic multi-metric analysis of demographic bias in machine learning models. Using face recognition as a controlled experimental setting, we evaluate model performance across multiple group partitions under a range of commonly used fairness metrics, including error-rate disparities and performance-based measures. Our results demonstrate that fairness assessments can vary significantly depending on the choice of metrics, leading to contradictory conclusions regarding model bias. To quantify this phenomenon, we introduce the Fairness Disagreement Index (FDI), a measure designed to capture the degree of inconsistency across fairness metrics. We further show that disagreement remains high across thresholds and model configurations. These findings highlight a critical limitation in current fairness evaluation practices and suggest that single-metric reporting is insufficient for reliable bias assessment.