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Biological tissues exhibit phase transitions governed by mechanical feedback between cells and their extracellular matrix (ECM). We demonstrate through bio-chemo-mechanical modeling that this emergent behavior arises from competing physical effects: increasing matrix stiffness enhances individual cell activation while simultaneously weakening long-range mechanical communication. This competition establishes a critical cell spacing threshold (80-160µm) that precisely matches experimental observations across diverse cell types and collagen densities. Our model reveals that the critical stretch ratio at which fibrous networks transition from compliant to strain-stiffening governs this threshold through the formation of tension bands between neighboring cells. These tension bands create a mechanical percolation network that drives the collective phase transition in tissue behavior. Our model explains how fibrous architecture controls emergent mechanical properties in biological systems and offers insight into both the physics of fiber-reinforced composite materials under active stress, and into potential mechanical interventions for fibrotic disorders.