Writing is not only a productive skill required in communication but it is also a tool for critical thinking, developing knowledge, and actualizing ideas and thoughts. This study aimed to examine the constraints that students faced due to various factors like cognitive style, critical thinking from the traditional angle and Digital Literacy from the modern angle, and their joint impact on students' argumentative writing skills. The population of the study comprised the 4th semester of the 2019 academic year, in the Faculty of Language and Letters, State University of Jakarta. A sample of 55 students was selected through a random sampling technique. Each of the four variables, cognitive style, critical thinking, digital literacy and argumentative writing skills, was tested through a questionnaire and a test. The data were analyzed statistically to determine the effect partially or simultaneously using SPSS. The results revealed that the average coefficient of determination of critical thinking cognitive style variables and digital literacy on argumentative writing skills got a relative less significant percentage of 2.2%, 13.1% and 10.6% respectively. It was also found that the influence of cognitive style on critical thinking was not directly visible. These two things do not directly show a significant effect between these variables. On the other hand, digital literacy also provided the same data. Digital literacy had no significant effect on students' argumentative writing skills. The study recommends more emphasis to be given on developing students cognitive, critical and argumentative skills in order to cope up with the challenges of digital literacy.