On last Friday's fellowship, the subject of Matriarchy of ancient China was brought up.
Out of suspicion, I could only take notes for further research.
After a brief referencing online, I have concluded that it is a minor thing that got spinned into a whole feminist propaganda.
First, there is Matrilineality; and there is Matriarchy. They are not the same thing. Matriarchy usually practices matrilineality, but not vice versa.
Matriarchy is a female dominant society.
Matrilineality is line of descendants traced via the mother side.
Although there is a group of Chinese called Musuo (摩梭), or Na, near Tibet, practicing matriarchy, there isn't much other evidence on this subject in Chinese history. Despite some theory that matrilineality had always been in China until the Shang Dynasty some 3,600 years ago. This theory based on the fact that the word (姓) has a female radical (部首) and the pattern of the meaning/type of characters used for the surname. This is of course, just a theory.
Some theory had gone even more absurd by saying that because the cavemen weren't smart enough to differentiate sexes or know enough biology to know there is a father, in addition to mother. Evolution could teach nothing useful but folly.