If — as her premise goes (no matter how erroneously) — women in Russia have certain privileges (i.e. are in a privileged position), then it makes no sense whatsoever to champion gender equality and thus risk losing these privileges.
This makes total sense in the practical, down-to-earth, instinctive sort of way (and I would have reasoned similarly regarding anything I would consider as my privilege), but of course it sounds laughably primitive when compared to the liberal Western discourse which tends to obsess over the immorality of privileges.