Semi-supervised learning is a promising method for medical image segmentation under limited annotation. However, the model cognitive bias impairs the segmentation performance, especially for edge regions. Furthermore, current mainstream semi-supervised medical image segmentation (SSMIS) methods lack designs to handle model bias. The neural network has a strong learning ability, but the cognitive bias will gradually deepen during the training, and it is difficult to correct itself. We propose a novel mutual correction framework (MCF) to explore network bias correction and improve the performance of SSMIS. Inspired by the plain contrast idea, MCF introduces two different subnets to explore and utilize the discrepancies between subnets to correct cognitive bias of the model. More concretely, a contrastive difference review (CDR) module is proposed to find out inconsistent prediction regions and perform a review training. Additionally, a dynamic competitive pseudo-label generation (DCPLG) module is proposed to evaluate the performance of subnets in real-time, dynamically selecting more reliable pseudo-labels. Experimental results on two medical image databases with different modalities (CT and MRI) show that our method achieves superior performance compared to several state-of-the-art methods. The code will be available at https://github.com/WYC-321/MCF.