In the poem "Siren Song," how does Margaret Atwood make use of mythology?

The ancient Greeks believed that sirens were creatures who lived on an island (and are often depicted as having bird bodies with female heads). These sirens would sing as sailors passed by on their ships, and, unable to resist the sound of their song, the sailors would steer into the rocks around the island, wrecking their ships and drowning.

Atwood's title, "Siren Song," is an allusion to these mythical creatures. In fact, the speaker of the poem is a siren herself. In the first lines, she says, 

This is the one song everyone
would like to learn: the song
that is irresistible:   (lines 1-3)

What makes this poem so compelling is that the reader does not realize that the "song" begins long before we think it does or expect it to. It begins with this first stanza, and we are roped in, hooked as the sailors would have been, because we do not think we are being manipulated. When she finally says, "I will tell the secret to you, / to you, only to you. / Come closer," we realize that we've been listening to the song all along and that she has us in her power (19-21). The last few lines make it clear that we've succumbed to her song, just like all who came before us. She says,

at last. Alas
it is a boring song
but it works every time. (25-27)

Cunningly, the song works on us because of the deep-seated human need to believe that we are special. We are unique. When she tells us these things, she gratifies our desire to think of ourselves in this way, and we are hers to command. It's really a fascinating take on the sirens themselves, but even more importantly, it reveals something crucial about the human condition: that we all want to feel special, and that this need is what makes us so easy to manipulate.