What would a book about the infinite variety and fluidity of the universe be without some gender-bending? It wouldn't be Ovid's Metamorphoses, that's for sure. Some of the poet's explorations of gender involve characters who have either mixed gender (like Hermaphroditus), or switch from one gender to the other (like Caenis who becomes Caenus, or Iphis who preserves her own gender-neutral name). At the same time, there are also more ambiguous characters, like Atalanta, who is interested in sports and hunting, but who otherwise fits female gender stereotypes, or Achilles, whose disguise as a girl can't conceal his stereotypically male interest in weapons. Whichever way you slice it, Ovid's poem has plenty to keep a modern gender-theorist theorizing into the wee hours of the morning.
Ovid is critical of excessive patriarchal authority.
Ovid is more sympathetic to female characters than male characters.