This paper introduces a formal framework for goal-hiding information-seeking dialogues to deal with interactions where a seeker agent estimates a human respondent to not be willing to share the sought-for information. Hence, the seeker postpones (hides) a sensitive goal topic until the respondent is perceived willing to talk about it. This regards a type of deceptive strategy to withhold information, e.g., a sensitive question, that, in a given dialogue state, may be harmful to a respondent, e.g., by violating privacy. The framework uses Quantitative Bipolar Argumentation Frameworks to assign willingness scores to topics, inferred from a respondent's asserted beliefs. A gradual semantics is introduced to handle changes in willingness scores based on relations among topics. The goal-hiding dialogue process is illustrated using an example inspired by primary healthcare nurses' strategies for collecting sensitive health information from patients.