The metals sector faces multiple and interconnected barriers to achieving circularity. This study examines steel, aluminum, and copper to illustrate how challenges vary between metals. While copper can often be recycled without quality loss, steel and aluminum face alloy-related limitations that drive downcycling and quality degradation. Using a matrix-based analytical framework, the study maps the interactions between economic, technological, institutional, and social constraints, distinguishing between primary drivers, secondary effects, feedback loops, and lock-in mechanisms. The results show strong reinforcing links between economic, technological, and institutional domains, with social factors playing a more indirect role. These findings align with observed industry patterns while adding a structured, quantitative perspective. By clarifying how different barriers combine and reinforce one another, the analysis identifies priority areas for intervention to advance metals recycling and support the transition toward a more circular economy.