The highest levels of reading literacy, as defined within PISA study, include the ability to use various cognitive skills, with argumentative skills being one of the most important among them. In the present study our goal was to reveal some of the factors that influence the development of argumentative skills in Serbian schools. We investigated the extent to which argumentative skills are required in PISA reading literacy tasks, as well as the specific difficulties our students have faced on these tasks, through an analysis of student performance. We also conducted an analysis of the educational practice - by doing in-depth interviews with teachers and content analysis of students' textbooks. The results revealed that: 1) Argumentations skills are an important requirement within PISA tasks; 2) Serbian students are mostly successful at basic tasks of recognizing arguments or providing arguments for the given position; they face difficulties answering the tasks which require precise formulation of relevant arguments as well as those demanding meta-cognitive skills (e.g. recognizing persuasive strategies in the given text). Their performance is particularly poor on tasks requiring the combination of information from different sources or information presented in different formats (text, tables, or graphs); 3) There is a significant gap between the requirements for argumentation skills our students usually encounter and PISA reading literacy tasks. In this paper we discuss some of the difficulties and obstacles to encouraging the development of argumentative thinking.