We consider a type of information-seeking dialogue between a seeker agent and a respondent agent, where the seeker estimates the respondent to not be willing to share a particular set of sought-after information. Hence, the seeker postpones (hides) its goal topic, related to the respondent's sensitive information, until the respondent is perceived as willing to talk about it. In the intermediate process, the seeker opens other topics to steer the dialogue tactfully towards the goal. Such dialogue strategies, which we refer to as goal-hiding strategies, are common in diverse contexts such as criminal interrogations and medical assessments, involving sensitive topics. Conversely, in malicious online interactions like social media extortion, similar strategies might aim to manipulate individuals into revealing information or agreeing to unfavorable terms. This paper proposes a formal dialogue framework for understanding goal-hiding strategies. The dialogue framework uses Quantitative Bipolar Argumentation Frameworks (QBAFs) to assign willingness scores to topics. An initial willingness for each topic is modified by considering how topics promote (support) or demote (attack) other topics. We introduce a method to identify relations among topics by considering a respondent's shared information. Finally, we introduce a gradual semantics to estimate changes in willingness as new topics are opened. Our formal analysis and empirical evaluation show the system's compliance with privacy-preserving safety properties. A formal understanding of goal-hiding strategies opens up a range of practical applications; For instance, a seeker agent may plan with goal-hiding to enhance privacy in human-agent interactions. Similarly, an observer agent (third-party) may be designed to enhance social media security by detecting goal-hiding strategies employed by users' interlocutors.