Motivation: Bioinformatics tools that predict protein stability changes upon point mutations have made a lot of progress in the last decades and have become accurate and fast enough to make computational mutagenesis experiments feasible, even on a proteome scale. Despite these achievements, they still suffer from important issues that must be solved to allow further improving their performances and utilizing them to deepen our insights into protein folding and stability mechanisms. One of these problems is their bias toward the learning datasets which, being dominated by destabilizing mutations, causes predictions to be better for destabilizing than for stabilizing mutations. Results: We thoroughly analyzed the biases in the prediction of folding free energy changes upon point mutations (ΔΔG0) and proposed some unbiased solutions. We started by constructing a dataset Ssym of experimentally measured ΔΔG0s with an equal number of stabilizing and destabilizing mutations, by collecting mutations for which the structure of both the wild-type and mutant protein is available. On this balanced dataset, we assessed the performances of 15 widely used ΔΔG0 predictors. After the astonishing observation that almost all these methods are strongly biased toward destabilizing mutations, especially those that use black-box machine learning, we proposed an elegant way to solve the bias issue by imposing physical symmetries under inverse mutations on the model structure, which we implemented in PoPMuSiCsym. This new predictor constitutes an efficient trade-off between accuracy and absence of biases. Some final considerations and suggestions for further improvement of the predictors are discussed. Supplementary information: Supplementary data are available at Bioinformatics online. Note: The article 10.1093/bioinformatics/bty340/, published alongside this paper, also addresses the problem of biases in protein stability change predictions.