Many readers see "They Flee from Me" as a poem in which normal Renaissance gender constructions are challenged. After the typical, male-dominated relationships of the first stanza, the second stanza flips to being female-dominated. Now the male seducer is the seduced, and the female is the aggressive hunter, seeking out her male prey. All these newfangled gender politics have our speaker totally baffled at the end of the poem, because he doesn't know what to do with a woman who doesn't quite fit the stereotypical female role.
"They Flee from Me" argues that gender roles are more flexible than fixed. Both men and woman can be dominant and passive.
Particularly in the first stanza, this poem suggests that fixed gender roles – "men are this, women are that" – is a way of reducing people to animals.