Nurturing the ability to argue is of great importance in science education, despite students often encountering cognitive and emotional barriers. The aim of this study was to examine the quality of argumentation and the issues raised by secondary school students when they are asked to respond to structured argumentation tasks. We chose topics from two different socio-scientific issues of varied perceived relevance to students’ daily lives: the sale of fast food in school canteens (Group 1) and the addition of antibiotics in animal feed (Group 2). The study involved 249 high school students aged 14–16, in Poland. A total of 139 participants took part in an intervention about fast food, and 110 in an intervention about the use of antibiotics. Data were collected in the form of written arguments developed by students as part of a structured teaching intervention. Quantitative and qualitative methods were used to process and analyze the data. On average, students’ arguments scored higher on the topic of antibiotic use on animal feed. Qualitative content analysis of the students’ arguments identified four thematic groups: (1) personal aspects revealing personal meanings, values, and defence mechanisms; (2) scientific aspects revealing substantive knowledge; (3) socio-cultural aspects revealing economic, sociological or cultural aspects; (4) nonsensical or incoherent arguments. A topic related to students’ personal decisions and perceived to be closest to their lives and daily experience (eating fast food in the school canteen) more often prompted arguments indicating cognitive defence, by denying the harmfulness of fast food and emphasizing possible advantages or appealing to the right to choose. Based on this finding, we discuss the need for defence mechanisms to be considered in pedagogical designs for the teaching of argumentation.