Logit-based knowledge distillation (KD) is commonly used to mitigate catastrophic forgetting in class-incremental learning (CIL) caused by data distribution shifts. However, the strict match of logit values between student and teacher models conflicts with the cross-entropy (CE) loss objective of learning new classes, leading to significant recency bias (i.e. unfairness). To address this issue, we rethink the overlooked limitations of KD-based methods through empirical analysis. Inspired by our findings, we introduce a plug-and-play pre-process method that normalizes the logits of both the student and teacher across all classes, rather than just the old classes, before distillation. This approach allows the student to focus on both old and new classes, capturing intrinsic inter-class relations from the teacher. By doing so, our method avoids the inherent conflict between KD and CE, maintaining fairness between old and new classes. Additionally, recognizing that overconfident teacher predictions can hinder the transfer of inter-class relations (i.e., dark knowledge), we extend our method to capture intra-class relations among different instances, ensuring fairness within old classes. Our method integrates seamlessly with existing logit-based KD approaches, consistently enhancing their performance across multiple CIL benchmarks without incurring additional training costs.