Overlap-based metrics such as the Dice Similarity Coefficient (DSC) penalize segmentation errors more heavily in smaller structures. As organ size differs by sex, this implies that a segmentation error of equal magnitude may result in lower DSCs in women due to their smaller average organ volumes compared to men. While previous work has examined sex-based differences in models or datasets, no study has yet investigated the potential bias introduced by the DSC itself. This study quantifies sex-based differences of the DSC and the normalized DSC in an idealized setting independent of specific models. We applied equally-sized synthetic errors to manual MRI annotations from 50 participants to ensure sex-based comparability. Even minimal errors (e.g., a 1 mm boundary shift) produced systematic DSC differences between sexes. For small structures, average DSC differences were around 0.03; for medium-sized structures around 0.01. Only large structures (i.e., lungs and liver) were mostly unaffected, with sex-based DSC differences close to zero. These findings underline that fairness studies using the DSC as an evaluation metric should not expect identical scores between men and women, as the metric itself introduces bias. A segmentation model may perform equally well across sexes in terms of error magnitude, even if observed DSC values suggest otherwise. Importantly, our work raises awareness of a previously underexplored source of sex-based differences in segmentation performance. One that arises not from model behavior, but from the metric itself. Recognizing this factor is essential for more accurate and fair evaluations in medical image analysis.