Against the backdrop of rapid advances in artificial intelligence, legal argument mining has emerged as an important research area linking legal texts with intelligent analysis, carrying significant theoretical and practical implications. Existing studies have primarily developed along three dimensions: data, technology, and theory. At the data level, raw legal texts and annotated corpora constitute the foundational resources. At the technological level, research paradigms have evolved from rule-based systems and traditional machine learning to large language models (LLMs). At the theoretical level, argumentation theory and legal dogmatics provide important references for modeling argumentation structures. However, despite ongoing progress, the overall development of legal argument mining remains relatively slow. Building on a systematic review of existing research, this study conducts an in-depth analysis and finds that this is due not only to data scarcity or technical limitations, but more fundamentally to the lack of a structured representational approach that reconciles theoretical expressiveness with computational feasibility. Specifically, this challenge manifests in dilemmas in data standardization, obstacles to effective modeling, and limitations in domain adaptation. In response, the study proposes several key directions for future research. It aims to provide a reframing of key problems and a pathway for future development in legal argument mining, while leaving specific models and implementation schemes for further investigation.