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We are not explicitly told why Alcinous does this, so we have to infer it from what has happened before.
Before Alcinous offers his daughter to Odysseus, Odysseus has told him two things. He has told of some of his trials in getting from Calypso's island to where he is. He has also told of how he did not want to come in to the palace with Nausikaa because he did not want to anger the king. Alcinous is pleased with what Odysseus says and he tells Odysseus
...now that I see what kind of person you are, and how much you think as I do, I wish you would stay here, marry my daughter, and become my son-in-law.
He seems to have been impressed with Odysseus's bravery and his manners.
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