There are sometimes conflicting definitions of gynocentrism, so we need to clarify a central facet of the word: the suffix -centrism.
What does the suffix mean?
The most accurate meaning of gynocentrism is that its a version of gender-narcissism (to useterm). Employing the word gynocentrism to discuss and/or advocate reciprocal exchanges between men and women, where women are occasional beneficiaries in certain ways, and men are beneficiaries in certain ways, is an erroneous use of the term because such exchanges, strictly speaking, do not constitute a gender “centrism” – ie. its not a gyno-centric relationship.
Said differently, being relationship-centered (eg. taking turns at helping or indulging each other) is the opposite to gender-centrism and gyno-centrism. Thus using gynocentrism to refer to something other than a gender-centrist relationship muddies the waters of definition.
Some people argue that patriarchy and gynocentrism are referring to precisely the same social contract, however the word patriarchy doesn’t have the -centrism suffix in it. Patriarchy is an -archy, but definitely not a -centrism.
In sum I can see little other reason for advocating gynocentrism than to appeal for more male chivalry and more pedestalization of women. This appears to be the reason for feminist appeals for gynocentrism.