A woman like that is not a woman, quite. I have been her kind. (6-7)
We're continuing with the dehumanizing kick here: our speaker's no longer a "thing," but she's not "quite" a woman. (In that case, what is she? Well, you've got us there, folks.) That's why the refrain packs such a punch – it comes as an assertion of collective identity after our speaker goes to great lengths to distance herself from all the things that we think of as acceptable womanly (or even human) behavior.
A woman like that is misunderstood. I have been her kind. (13-14)
Hmmm…sound familiar? Sexton moves her speaker into a position of outsider-ness before asserting her unity with that particular form of outsider-ness. There are some small differences between the first stanza and the second, however. For one thing, stanza one takes the speakers' weirdness as a fact. Stanza two shifts perspective slightly – now it's not necessarily the speaker who's categorically crazy. She's just misunderstood. Maybe she's nuts…but maybe it's society that thinks she's nuts. There's a difference.
A woman like that is not ashamed to die. I have been her kind. (20-21)
Third time's the charm, folks. By the time we've been through this refrain a few times, it starts to sound heroic. Plus, we've moved from what others think about our speaker to what she herself feels about her choices. In a strange way, this is the closest we get to understanding her feelings.