Biometric data embeds information about the user which enables transparent and frictionless authentication. Despite being a more reliable alternative to traditional knowledge-based mechanisms, sharing the biometric template with third-parties raises privacy concerns for the user. Recent research has shown how biometric traces can be used to infer sensitive attributes like medical conditions or soft biometrics, e.g. age and gender. In this work, we investigate a novel methodology for private feature extraction in online biometric authentication. We aim to suppress soft biometrics, i.e. age and gender, while boosting the identification potential of the input trace. To this extent, we devise a min-max loss function which combines a siamese network for authentication and a predictor for private attribute inference. The multi-objective loss function harnesses the output of the predictor through adversarial optimization and gradient flipping to maximize the final gain. We empirically evaluate our model on gait data extracted from accelerometer and gyroscope sensors: our experiments show a drop from 73% to 52% accuracy for gender classification while loosing around 6% in the identity verification task. Our work demonstrates that a better trade-off between privacy and utility in biometric authentication is not only desirable but feasible.