Chinese Text Error Correction (CTEC) aims to detect and correct errors in the input text, which benefits human daily life and various downstream tasks. Recent approaches mainly employ Pre-trained Language Models (PLMs) to resolve CTEC. Although PLMs have achieved remarkable success in CTEC, we argue that previous studies still overlook the importance of human thinking patterns. To enhance the development of PLMs for CTEC, inspired by humans' daily error-correcting behavior, we propose a novel model-agnostic progressive learning framework, named ProTEC, which guides PLMs-based CTEC models to learn to correct like humans. During the training process, ProTEC guides the model to learn text error correction by incorporating these sub-tasks into a progressive paradigm. During the inference process, the model completes these sub-tasks in turn to generate the correction results. Extensive experiments and detailed analyses demonstrate the effectiveness and efficiency of our proposed model-agnostic ProTEC framework.