This study examines the structure of student argumentation on artificial intelligence (AI) within the framework of the Toulmin model. We analyzed essays on AI written by 452 Hungarian secondary school students, coding for the presence of the six Toulmin components (claim, data, warrant, backing, qualifier, rebuttal). The results show that students frequently use fundamental argumentation components such as claim, data, and rebuttal. However, elements that provide deeper, more nuanced argumentation, such as backing and qualifiers, appear rarely. Using hierarchical cluster analysis, we identified three distinct argumentation profiles: Critical Arguers, who construct complex structures that also reflect on counterarguments; Minimal Arguers, who follow a simplified, primarily claim-based strategy; and Direct Rebutters, who employ a confrontational style of argumentation that omits the warrant but focuses on rebuttal. Based on our findings, we propose differentiated pedagogical strategies to foster the development of critical thinking in students with different argumentation styles.