Since the second half of the 20th century, many areas of humanities, which sought to combine their efforts in researching various social phenomena, have been rapidly developing. It is about theories of argumentation, communication, practical philosophy, psychology, behavioral economics, etc. On the one hand, the factors that prevent a person from acting rationally are analyzed, and on the other hand, various techniques for achieving success by a person in communication, activities, etc., are developed. To date, many cognitive biases or illusions have been established, under the influence of which a person usually does not act rationally. The authors of the publication (Pohl, 2004) divide cognitive illusions into three groups: thinking, judgment, and memory. They consider confirmation bias as an illusion of thinking. In this regard, it is promising to investigate this bias in the context of the modern argumentation theory, the sources of which were historically such ancient disciplines as logic, dialectics, and rhetoric.