That all makes sense to me. We should add that the title is sometimes seen to include "there may be a reason why", which could also be the first line of the poem, perhaps affecting the interpretation. Many online sites show a different formatting, and even different lines with capital letters, possibly important but likely not.
Still, it seems to be in the format of a riddle, no? We are asked to guess what/who the speaker is, even though s/he identifies hermself as a beautiful woman along with other identities. If that is so, I would guess the solution to the riddle as Gaia (earth mother).
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