In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within such arguments. The study is based on semi-structured interviews with 19 preservice mathematics teachers from Mexico. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (1) mathematics is related to the development of mental or thinking skills, (2) mathematics is useful for daily life, and (3) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (1) the myth of reference, (2) the myth of participation, (3) the myth of importance, and (4) the myth of cognitive development. The report concludes by discussing the results and pointing out some future research routes.