Lurking at the heart of this ancient epic of bronze age barbarian valor, there is much in the text to support egalitarian ideas for both sexes. Draupadi’s svayamvara story has an overt story thread of macho vanity. The hero grabs his weapon, wins the woman, sheds his garb of a sage holy man and becomes a bad-ass warrior. Lurking underneath this is the subversion of the overt chauvinism. The story of Draupadi who throws caution to the wind and marries the imposter jokester given a chance in the martial contest for kicks and grins after a day of mounting frustration for the entrants. King Drupada obviously sabotaged them - creating a bow for the contest that was never softened and remains inflexibly hard piece of wood in the shape of a bow. Draupadi thumbs her nose and marries a non-warrior, her defiance in forcefully rejecting Karna and standing up for herself to the end is a transformative example for the Pandavas. The five brothers following her lead go from members of the audience to hero of the epic in a few strides.
