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Peer-argumentation is an effective learning activity, yet difficult to enact at scale. While Pedagogical Conversational Agents (PCAs) have been widely studied, their role as arguing peers that engage students in dialogic argumentation remains under-explored. We present ArgueMate, an arguing agent designed to support peer-argumentation exercises by deliberately maximising disagreement based on students’ initial positions. We adopted a user-centred design approach, conducting design interviews with 10 university students to identify key user requirements. Informed by these insights, we implemented an initial prototype featuring two argumentation styles—collaborative and competitive—and explored its use in a formative classroom study with 16 students. Results highlight how maximised disagreement can foster engagement and productive argumentation while also revealing trade-offs between collaborative and competitive agent behaviours. This paper reports early-stage findings that surface design tensions around agent argumentation style, stance-taking, and student engagement, and contributes design insights for future PCA to support argumentation-based learning at scale.