Human users tend to selectively ignore information that contradicts their pre-existing beliefs or opinions in their process of information seeking. These “self-imposed filter bubbles” (SFB) pose a significant challenge for cooperative argumentative dialogue systems aiming to build an unbiased opinion and a better understanding of the topic at hand. To address this issue, we develop a strategy for overcoming users’ SFB within the course of the interaction. By continuously modeling the user’s position in relation to the SFB, we are able to identify the respective arguments which maximize the probability to get outside the SFB and present them to the user. We implemented this approach in an argumentative dialogue system and evaluated in a laboratory user study with 60 participants to show its validity and applicability. The findings suggest that the strategy was successful in breaking users’ SFBs and promoting a more reflective and comprehensive discussion of the topic.