Critical thinking (CT), a 21st-century skill, not only plays a crucial role in students’ academic success but is also a fundamental capacity increasingly sought upon in the competitive global job market. However, there has been limited research in Vietnam on how to foster CT through English language teaching in higher education. This study fills this gap by investigating the challenges of teaching CT through the teaching of four English practical skills at the University of Foreign Language Studies - the University of Da Nang (UFLS-UD) via the Pathways Listening, Speaking, and Critical Thinking (2nd edition), which is a global, innovative academic English coursebook series carefully designed to develop integrated English language skills and CT. Coursebooks have been used in the curriculum at the Faculty of English and the Faculty of Foreign Language Teacher Education since 2021. However, how to effectively explore coursebooks’ resources to develop students’ critical thinking skills has not been investigated. With the employment of research methods, namely, survey questionnaires and semi-structured interviews, our study is an attempt to identify the abovementioned challenges, thereby suggesting solutions to enhance the quality of teaching CT combined with language skills for English-majored students.