In Book 13 of The Odyssey, why does Athena test Odysseus?
I think there are two elements two think about in answering this question. Firstly, the gods in both The Iliad and The Odyssey are shown to be quite a fickle group, using their human heroes to champion their petty squabbles against other gods and treating them as playthings. Thus, in a sense, Athena can test her hero because she is a goddess and she can do what she likes.
However, also, it is important to remember what kind of character Odysseus is. He is not known as "the wily Odysseus" for nothing, and certainly throughout the rest of the book disguise, deception and illusion are used readily and frequently to trick, beguile and deceive. Thus, there is something fitting in Odysseus not realising he has reached Ithaca in this book: the deceiver is himself deceived. Of course, once Odysseus realises his location, he immediately determines to employ deception to achieve his goal until the grey-eyed goddess Athena reveals truth through her own act of self-revelation.