In the present article, we investigate personality traits that may lead a respondent to refuse to answer a forced-choice personality item. For this purpose, we use forced-choice items with an adapted response format. As in a traditional forced-choice item, the respondent is instructed to choose one out of two statements to describe their personality. However, we also offer the respondent the option of refusing to choose. In this case, however, the respondent must report a reason for refusing to choose, indicating either that the two statements describe them equally well, or that neither statement describes them adequately. We use an Item Response Tree (IRTree) model to simultaneously model refusal to choose and the reason indicated by the respondent. Our findings indicate that respondents who score high on openness are more likely to refuse to choose, and they tend to identify more often with both statements in the forced-choice item. Items containing non-socially desirable statements tend to be skipped more often, with the given reason being that neither proposition describes the respondent well. This tendency is stronger among respondents who score high on agreeableness, that is, a trait that is typically related to social desirability. We discuss the theoretical and practical implications of our findings.