Evidence-aware fake news detection aims to conduct reasoning between news and evidence, which is retrieved based on news content, to find uniformity or inconsistency. However, we find evidence-aware detection models suffer from biases, i.e., spurious correlations between news/evidence contents and true/fake news labels, and are hard to be generalized to Out-Of-Distribution (OOD) situations. To deal with this, we propose a novel Dual Adversarial Learning (DAL) approach. We incorporate news-aspect and evidence-aspect debiasing discriminators, whose targets are both true/fake news labels, in DAL. Then, DAL reversely optimizes news-aspect and evidence-aspect debiasing discriminators to mitigate the impact of news and evidence content biases. At the same time, DAL also optimizes the main fake news predictor, so that the news-evidence interaction module can be learned. This process allows us to teach evidence-aware fake news detection models to better conduct news-evidence reasoning, and minimize the impact of content biases. To be noted, our proposed DAL approach is a plug-and-play module that works well with existing backbones. We conduct comprehensive experiments under two OOD settings, and plug DAL in four evidence-aware fake news detection backbones. Results demonstrate that, DAL significantly and stably outperforms the original backbones and some competitive debiasing methods.