The article deals with the problem of the cognitive nature of metaphor formed in the medium of mythological consciousness of the primitive human. It is supposed that such the main features of the mythological thinking as sensory concreteness and inability to form abstract notions caused the nature of the primary metaphor which was formed through the cognitive mechanism of analogy the surrounding objects and phenomena, and the inner mental states of the human – this metaphor was not linguistic, but concrete and sensory. It is ascertained that the direction of metaphorization in the primitive consciousness was inverted to modern one, because the modern people mind uses more intelligible concrete concepts to express abstract concepts, but the primitive humans conceiving themselves as a part of the nature and understanding their inner world as the outer one projected their inner states, which are comprehended as abstract now, onto the natural phenomena, which can be perceived through the organs of sense. It is argued that formation of critical abstract thinking is related with the development of the human cognitive abilities, what caused the metaphorization veer and also the transition from the mythological mind to linguistic one. It is analyzed three approaches to solving the problem of the relation between language and myth where an important argument was the metaphoricity both of thinking and language: 1) the linguistic theory of myth by M. Müller according to which the loss initial sense of the linguistic metaphor generated myth; 2) the theory of myth based not on the linguistic metaphor, but on the concrete sensory analogy of the real objects and human perceptions (E. Tylor, A. Potebnya); 3) Neo-Kantian theory by E. Cassirer which postulates the simultaneous development of language and myth which have the common sources. It is proved that metaphoricity is inherent in the human mind of every historical period, because the linguistic metaphor is based on the cognitive one, that is the latter makes it possible to comprehend the world and ourselves in this world and express the obtained knowledge by means of language. At the same time, metaphoricity and abstractness of thinking are harmonious processes which provides the productive cognizing of the world and the creative working its results out through the fixation of them in the linguistic forms.