Numerous algorithms have been developed for Conditional Average Treatment Effect (CATE) estimation. In this paper, we first highlight a common issue where many algorithms exhibit inconsistent learning behavior for the same instance across different group assignments. We introduce a metric to quantify and visualize this inconsistency. Next, we present a theoretical analysis showing that this inconsistency indeed contributes to higher test errors and cannot be resolved through conventional machine learning techniques. To address this problem, we propose a general method called \textbf{Consistent Labeling Across Group Assignments} (CLAGA), which eliminates the inconsistency and is applicable to any existing CATE estimation algorithm. Experiments on both synthetic and real-world datasets demonstrate significant performance improvements with CLAGA.