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This work presents a systematic investigation into the trustworthiness of explanations generated by self-interpretable graph neural networks (GNNs), revealing why models trained with different random seeds yield inconsistent explanations. We identify redundancy—resulting from weak conciseness constraints—as the root cause of both explanation inconsistency and its associated inaccuracy, ultimately hindering user trust and limiting GNN deployment in high-stakes applications. Our analysis demonstrates that redundancy is difficult to eliminate; however, a simple ensemble strategy can mitigate its detrimental effects. We validate our findings through extensive experiments across diverse datasets, model architectures, and self-interpretable GNN frameworks, providing a benchmark to guide future research on addressing redundancy and advancing GNN deployment in critical domains. Our code is available at \url{https://github.com/ICDM-UESTC/TrustworthyExplanation}.