The first goal of this article is to explain the social and psychological mechanisms inherent in reaching an agreement within groups with highly divergent initial opinions. The second goal is to diagnose possible antagonistic processes in such groups. The empirical data used were obtained from recordings of focus group interviews, conducted with parents of school age children discussing the issue of sexual education in schools. The results suggest that revealing world views that justify claims made in the debate can foster agreement when the following conditions are met: (1) There exists at least some common ground in the group to serve as a starting point for agreement in other areas; (2) The articulation of different world views is not negatively evaluated or diminished by others in the group; (3) Disputants argue in their opponents' way of thinking. Another result observed is that processes other than rational analyses of the controversy can take place and can lead to agreement.