The male / female + mortal / immortal pairing of dichotomies comes up again on Ogygia and is introduced via the reference to Tithonus at the beginning of the book.

Odysseus / male / mortal

Calypso / female / immortal

Tithonus / male / immortal but always aging, punished for Calypso's request to make her partner immortal

The major theme of the allusion is that mortals must accept their mortality, and that doing so is the only way to achieve authentic selfhood.

The male / female dichotomy is incorporated into the mortal / immortal theme when Calypso offers to help Odysseus sail home, but points out that if he stays on Ogygia, she will always be beautiful (that and the island itself is a worry-free paradise). Odysseus cleverly sidesteps her jealousy by acknowledging that his wife now will be old and unattractive, but he misses the smoke from his hearth--that oikos theme. But this isn't hearth vs. gender; Penelope is still Odysseus' love (and equal in metis), and his primary reason for returning. He simply wants to leave without incurring Calypso's wrath.

Calypso / female / immortal

Penelope / female / mortal

The Odysseus-Penelope bond (as Homer depicts it) suggests, in my view, the overcoming of gender hierarchy / domination / violence, not the support of it, and that bonding is a prerequisite to achieving authentic selfhood.

The locus classicus for the promotion of gender hierarchy over gender unity is The Aeneid (though Virgil does portray the necessity of domination as tragic).