Answer:
The answer to the question: Who says the following and why? "Farewell, my friend! And when you are at home, home in your own land, remember me at times. Mainly to me you owe the gift of life.", would be:
1. Who says those words? Nausicaa, the Phaeacian princess whom Odysseus meets when he ends up stranded on the Phaeacian´s land, and who has welcomed him and honored him. This happens in book 8 of "The Odyssey" by Homer. Odysseus has been already offered once to forget all about who he is, and his final goal, in the name of pleasure, riches and power. But, once more, like he did with Calypso, Odysseus refuses both the king and the princess of the Phaeacians.
2. Why did she say those words? Because she wanted to marry Odysseus, and her hand had been offered to him not just by her father, but by the girl herself. However, Odysseus refuses and the girl makes one last attempt by guilting him into accepting. By stating: "you owe the gift of life", Nausicaa is reminding Odysseus that he has a debt with her, and therefore, as payment, should give himself to her. He takes her words, all of them, quite literally, and promises to worhsip her once he returns home to Ithaca.
