Self-improvement through post-training methods such as iterative preference learning has been acclaimed for enhancing the problem-solving capabilities~(e.g., mathematical reasoning) of Large Language Models~(LLMs) without human intervention. However, as exploration deepens, it becomes crucial to assess whether these improvements genuinely signify progress in solving more challenging problems or if they could lead to unintended regressions. To address this, we propose a comprehensive evaluative framework that goes beyond the superficial pass@1 metric to scrutinize the underlying enhancements of post-training paradigms for self-improvement. Through rigorous experimentation and analysis across diverse problem-solving tasks, the empirical results point out the phenomenon of \emph{self-improvement reversal}, where models showing improved performance across benchmarks will paradoxically exhibit declines in broader, essential capabilities, like output diversity and out-of-distribution~(OOD) generalization. These findings indicate that current self-improvement practices through post-training are inadequate for equipping models to tackle more complex problems. Furthermore, they underscore the necessity of our critical evaluation metrics in discerning the \emph{progress or regress} dichotomy for self-improving LLMs.