The task of text-to-SQL aims to convert a natural language question into its corresponding SQL query within the context of relational tables. Existing text-to-SQL parsers generate a "plausible" SQL query for an arbitrary user question, thereby failing to correctly handle problematic user questions. To formalize this problem, we conduct a preliminary study on the observed ambiguous and unanswerable cases in text-to-SQL and summarize them into 6 feature categories. Correspondingly, we identify the causes behind each category and propose requirements for handling ambiguous and unanswerable questions. Following this study, we propose a simple yet effective counterfactual example generation approach that automatically produces ambiguous and unanswerable text-to-SQL examples. Furthermore, we propose a weakly supervised DTE (Detecting-Then-Explaining) model for error detection, localization, and explanation. Experimental results show that our model achieves the best result on both real-world examples and generated examples compared with various baselines. We release our data and code at: \href{https://github.com/wbbeyourself/DTE}{https://github.com/wbbeyourself/DTE}.
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