This study aimed to examine the cognitive strategies of critical thinking in high school students' argumentative writing. Despite extensive research on critical thinking and argumentative writing, there is a lack of in-depth analysis of the specific cognitive strategies employed by high school students in their argumentative essays. Using a case study approach, data from 120 students at SMAN 2 Wonosari were collected through document analysis. Four findings related to the cognitive strategy of critical thinking were obtained in this study. (1) Interpretation is realised through the author's point of view and the formation of definitions, with positions expressed as either opposition or support. (2) The analysis was conducted by identifying the components and structure of arguments, where components included premises and conclusions, and structures were categorised as simple or complex arguments. (3) Inference is achieved through deductive and inductive reasoning. Deductive reasoning follows general patterns, such as chained arguments, modus ponens, and modus tollens, whereas inductive reasoning involves generalisation and causality. (4) The evaluation focuses on accuracy and logical correctness, with accuracy determined by the truth of the premises and logical correctness assessed through valid and strong arguments. The findings serve as a crucial resource for educators and students to enhance critical thinking skills in academic writing, potentially leading to improved teaching methods and student performance in argumentative essay writing.