The term, gynocentrism is a shorthand for white knight or plain chivalrous behaviour on a societal scale. In other words, putting women before anything else in politics and society, often to the detriment of other groups.
Modern gynocentrism can arguably be traced back to late-Middle-Age France.
Gynocentrism, if it were in common practice actually an antonym of androcentrism, would mean the belief that the world should order itself around feminine gender traits (sensitivity, gentleness, gossip, leeching, dishonesty, and empathy). However a word to describe that does not exist yet unfortunately, despite it also being a common belief.
Gynocentrism often means purported ideology spurring policies, institutions and ordinances that are said to disproportionately favor women over men, or the idea Modern MRAs as well as masculinists think that society has become so gynocentric that it has sparked mass misandry. Indeed, the media for example, in the western world is very gynocentric. A person who holds gynocentric views is a gynocentrist.
Women have always been the primary victims of war. Women lose their husbands, their fathers, their sons in combat - Hillary Clinton.
The medical field for example, solely studies gynecology and is silent on adrology, the counterpart field dealing with male health. The term gynecology on google search produces 67 million search returns, whilst andrology produces only a tenth of those search returns. JSTOR is even more lopsided, with search returns producing almost 8000% more returns for women than for men when combining the spellings of "gynaecology" and "gynecology". Where's the egalitarianism in the light of andrological issues such as tesicular cancer, prostate cancer and MGM?
Further indicators of a societal tendencies towards gynocentrism include widespread bias against males in the legal system. For instance, Sonja Starr of the University of Michigan Law School, in a paper published in 2012 found evidence of "large gender gaps favoring women throughout the sentence length distribution (averaging over 60%), conditional on arrest offense, criminal history, and other pre-charge observables. Female arrestees are also significantly likelier to avoid charges and convictions entirely, and twice as likely to avoid incarceration if convicted."  Another paper by Rehavi & Starr (2012) found that blacks on average received a 10% longer sentence than whites in the United States.  Thus, by synthesising the findings of the two papers, one can conclude that gender bias against men in the American court system (in terms of sentence length) is 6x greater than the effects of racial bias on sentencing, controlling for criminal history, and the severity of the offence.
Another particularly striking examine of gynocentrism is the concept of "femicide". Although defined by feminists as "" all gender-related killings of women, motivated by systematic discrimination against and devaluing of women and girls."  the functional purpose of this construct is to legally regard the murders of women as more grevious, and therefore deserving of harsher punishment and greater enforcement than similar acts committed against males. Feminists in various countries, notably Spain and France  have campaigned to have "femicide" recognized as a unique social problem that deserves harsher punishment and greater consideration than similar crimes perpetrated crimes against men.
- Conference on domestic violence in San Salvador, El Salvador (17 November 1998): https://web.archive.org/web/20010726225357/http://clinton3.nara.gov/WH/EOP/First_Lady/html/generalspeeches/1998/19981117.html