The stuff that we usually hear that girls reach maturity early or women complain that there are fewer restrictions on boys or that girls are well behaved can be used to conclude that women are more obedient than men. The researches say otherwise but a simple explanation from an article using various studies (which also says both genders have the same level of obedience) quotes "Navarrete et al. (2012) offer an evolutionary theory called the "Male Warrior Hypothesis". They suggest that males have evolved to be hostile towards outsiders but females have evolved a "tend-and-befriend" response instead. Navarrete links this to behaviour in chimpanzees, where the males launch attacks on rival groups of chimps." So how do you befriend someone? Show them respect, accept to some of their demands, try to impress them? Could it be confused with the definition of obedience (compliance with an order, request, or law or submission to another's authority.)? These do fit somewhat.

Also, the saying "women are always right" which has been used as some jokes throughout our history is somewhat opposite to this nature of obedience (if they obey more shouldn't they also easily accept their mistakes to not upset others?) or Does it stem from this nature itself? How does this stem from the befriending nature that you ask or ponder? It could be attributed that if you want to be loved by someone badly, you will not want to upset them at any cost. So if you do something wrong, you will want to deny it outright not to be seen as a bad person as cited here "Results showed that females exhibit higher rejection sensitivity and interpersonal anxiety than males. In general, females appear to experience higher anxiety than males, and they are also more likely to develop anxiety disorders ."