I don't have sources for what I am about to discuss, so I will state here that this comes from years of reading about Athena, the opinions of fellow pagans and books about Athena and how she has been interpreted over the years in our modern culture.
That's pretty normal, after all, all religion, myth, and history get interpreted by us, whether we like to admit it or not, and one of the interpretations, and not a very common one, but one that makes sense in a culture as entrenched in monotheism as our is.
For some, Zeus is conflated with Jehovah or Yahweh (or Allah, though most Moslems would likely take offense to that) and as such, the concept of Athena, the notion of a goddess of wisdom, is seen as the manifestation of the Wisdom of Zeus. That is to say, that Athena is, essentially, part of the godhead that is Zeus in much the same way that Jesus and the Holy Spirit are part of the same godhead as Jehovah.
I call this theological reductionism.
This is actually part of several religious paradigms. Perhaps the biggest religion to express similar ideas is Christianity, with the holy trinity, but Christianity does not refer to the aspects of God as Gods, as it goes against the idea of a monotheistic theology, but it is Hinduism that most makes use of this concept with many theologies expressing the notion that all the Devas/Gods are aspect of a greater being, of a greater reality.
The Greeks too had a similar concept, though the Greeks did not reduce their deities to a singularity, instead they accepted the idea that Gods appeared to different people in different ways, and they used epithets (titles) to make these distinctions.
So, what does it mean for Athena to be seen this way? Does it mean Athena does not exist? That Athena is just an aspect of Zeus?
Well, no! See, the cults of the Gods are fractured, always have been, and even in the most monotheistic of religions, there is fracture and difference in interpretation, so it is not odd at all that some people, especially people not vested in the Gods as the sources of veneration, like scholars, to see the Gods in these ways especially considering that the worshippers of these Gods themselves have trouble agreeing on the theological realities of the Gods themselves.
It is also not at all odd that a God like Zeus would have manifestations that would seem like other Gods, and when I try to explain such things, I think of them differently. I tend to think of these manifestations as angeloi (the word means angels) and so I can categorize these small aspects so as to not cause internal confusion.
Zeus is the greatest of the Pan Hellenic Gods. He was worshipped all over the Greek speaking lands, and more so, as the indo-european sky father, very similar deities were worshipped by peoples all over the North Mediterranean. Even among the Semitic people, the Sky Father was a powerful force, one which we see even today in Allah and Yahweh, and as such he was worshipped and given cult all over the land, and in these different lands he was given different titles which went along with the cultural values of the people who offered worship.
But all of these different cults, even those that were Greek, had their own ways of seeing the God, and even in a city, different tribes and families could have slightly different ways of seeing him. This leads us to how, for example, the Goddess we know as Athena could have come to be seen as being born from the head of Zeus rather than being born of the land, as one might imagine her to be given a more indigenous myth.
When the tribes of Indo-Europeans, with their Sky God, migrated into greece, slowly supplanting the local culture with a version of their own, one in which the two cultures blended, the Sky God we know as Zeus supplanted the local deities, one imagines they were mostly Goddesses, and in most cases, it was said that Zeus married them, but Athena is a special case, because even as Athens slowly grew, the people of that land were not likely to accept her as wife of Zeus. Maybe they saw her as a maiden, or maybe their local culture was too entrenched and they could not see her as being married to the God of foreigners, whatever the case, she developed not into the wife, mistress, or victim of Zeus, but into his daughter, and even then, she was seen as having been born of him directly rather than from her mother, Metis.
As Hellenic culture developed, the myths around her became strangely masculinized, and her association with Wisdom became set into the religious beliefs of the Greeks, because as the power of Athens grew, so did the influence of its divine patron, and as such it became more and more a necessity for this strongly patriarchal culture to tie her closer and closer to Zeus, and in many ways, it was due to this that this idea that Athena was the Wisdom of Zeus (and that Apollo, a God of Prophecy, was simply speaking the prophecies of Zeus) became a possibility in this religion.
So, I will give you my personal take, because that is all I can give you, and tell you that all Gods are wise.
ALL OF THEM!
So, when we say that Athena is the Goddess of Wisdom, what does that mean? Does it mean she is the wisest? No. Does it mean she holds the keys to wisdom? No. It means that it was to Athena that the people turned when they needed wisdom, when they felt that divine wisdom was needed to overcome an issue, to make a decision, etc., but this was not a universal thing, because different situations needed different kinds of Wisdom, and maybe when dealing with the cultivation of grains, it was Demeter's wisdom that was needed, and when dealing with matters of the heart the wisdom of Aphrodite, so perhaps what it means that Athena was the Goddess of Wisdom was that in her city, the city that worshipped her above others, she inspired learning and the cultivation of wisdom, and as such, the title stuck and people turned to her more and more for this wisdom.
And maybe, just maybe, some people turned to her and asked that she intercede with Zeus and help bring them his wisdom as well.
