Entity matching is a critical problem in data integration, central to tasks like fuzzy joins for tuple enrichment. Traditional approaches have focused on overcoming fuzzy term representations through methods such as edit distance, Jaccard similarity, and more recently, embeddings and deep neural networks, including advancements from large language models (LLMs) like GPT. However, when integrating with external databases, the core challenge in entity matching extends beyond term fuzziness to the ambiguity in defining what constitutes a "match". This is because external databases contain tuples with varying levels of detail and granularity among entities, and an "exact match" in traditional entity matching rarely happens. As a result, understanding how entities are related and the potential nuances is critical, especially for high-stake tasks for responsible AI. In this work, we study a case problem of entity matching for ESG reporting. We propose a novel approach that shifts focus from purely identifying semantic similarities to understanding and defining the "relations" between entities for resolving ambiguities in matching, with a human-in-the-loop process to make the final decision. By pre-defining a set of relations relevant to the task at hand, our method allows analysts to navigate the spectrum of similarity more effectively, from exact matches to conceptually related entities, and responsibly perform downstream tasks.