Interactive argument pair identification is an emerging research task for argument mining, aiming to identify whether two arguments are interactively related. It is pointed out that the context of the argument is essential to improve identification performance. However, current context-based methods achieve limited improvements since the entire context typically contains much irrelevant information. In this paper, we propose a simple contrastive learning framework to solve this problem by extracting valuable information from the context. This framework can construct hard argument-context samples and obtain a robust and uniform representation by introducing contrastive learning. We also propose an argument-context extraction module to enhance information extraction by discarding irrelevant blocks. The experimental results show that our method achieves the state-of-the-art performance on the benchmark dataset. Further analysis demonstrates the effectiveness of our proposed modules and visually displays more compact semantic representations.