Social matching is a task that recommends potential friends to users based on their existing friendships. This user-to-user recommendation setting extends general recommender systems by shifting the focus from user-item interactions to interactions among users themselves, and general recommendation methods are often directly applied to this setting. However, we argue that in federated learning, directly applying existing federated recommendation methods to social matching can result in privacy leakage, due to the specificity of social matching: the mutual nature of friendships. We theoretically and quantitatively reveal these security vulnerabilities and propose a novel interaction-level membership inference attack targeting federated social matching. Our attack employs a reconstruction model combining affine transformations with an MLP to capture both linear and non-linear mappings between users' public and private embeddings. Trained on a portion of leaking user data, it can reconstruct benign users' private embeddings and infer their true friends. We conduct numerous experiments on multiple datasets under various experimental settings to verify the effectiveness and robustness of our attack method. Experimental results show that: (i) Our attack approach exhibits strong robustness and effectiveness across diverse experimental setups; (ii) Existing defense methods fail to effectively resist our attack while maintaining satisfactory recommendation performance. Our findings highlight the need for new privacy-preserving techniques specifically designed for federated social matching.