Sentence transformers excel at grouping topically similar texts, but struggle to differentiate opposing viewpoints on the same topic. This shortcoming hinders their utility in applications where understanding nuanced differences in opinion is essential, such as those related to social and political discourse analysis. This paper addresses this issue by fine-tuning sentence transformers with arguments for and against human-generated controversial claims. We demonstrate how our fine-tuned model enhances the utility of sentence transformers for social computing tasks such as opinion mining and stance detection. We elaborate that applying stance-aware sentence transformers to opinion mining is a more computationally efficient and robust approach in comparison to the classic classification-based approaches.