Continual semantic segmentation (CSS) is a cornerstone task in computer vision that enables a large number of downstream applications, but faces the catastrophic forgetting challenge. In conventional class-incremental semantic segmentation (CISS) frameworks using Softmax-based classification heads, catastrophic forgetting originates from Catastrophic forgetting and task affiliation probability. We formulate these problems and provide a theoretical analysis to more deeply understand the limitations in existing CISS methods, particularly Strict Parameter Isolation (SPI). To address these challenges, we follow a dual-phase intuition from human annotators, and introduce Cognitive Cascade Segmentation (CogCaS), a novel dual-phase cascade formulation for CSS tasks in the CISS setting. By decoupling the task into class-existence detection and class-specific segmentation, CogCaS enables more effective continual learning, preserving previously learned knowledge while incorporating new classes. Using two benchmark datasets PASCAL VOC 2012 and ADE20K, we have shown significant improvements in a variety of challenging scenarios, particularly those with long sequence of incremental tasks, when compared to exsiting state-of-the-art methods. Our code will be made publicly available upon paper acceptance.