Why did they move from matriarch to patriarchy?

This is due to the fact that the role of men in society began to grow with the development of crafts and economy. Thus, the dominant role in society gradually began to pass to the man. Over time, the patriarchy was able to completely push back matriarchy. The formation of patriarchy led society to the emergence of class inequality, to the establishment of a slave system, as well as to the emergence of the first despotic states.