My question is about free will in Greek mythology. How do we explain that fate is also a thing while they also have free will?
The answer really depends on to which interpretation of free will you subscribe. I will greatly oversimplify the various philosophical interpretations of free will here into two camps:
Compatibilism is the belief that free will and determinism are mutually compatible and that it is possible to believe in both without being logically inconsistent. The oldest Greek school of philosophy that proposed this belief is stoicism
Incompatibilism is the view that a deterministic universe is completely at odds with the notion that persons have a free will; that there is a dichotomy between determinism and free will where philosophers must choose one or the other. In Ancient Greece, this would be more a religious view than a philosophy, i.e. our lives, to the tiniest detail, are written or spun by the fates
These two camps can be rendered into the following philosophical interpretations:
Hard determinism (determinism + incompatibilism)
Deterministic compatibilism (determinism + compatibilism)
Indeterminism/metaphysical libertarianism (indeterminism + incompatibilism)
Both Hard Determinism and Deterministic compatibilism existed in some form in Greek philosophy or religion. If for example we look at Oedipus, you can interpret the story with both of these perspectives. Indeterminism is more of a 20th-century philosophy.
Oedipus is a tragic hero, who accidentally fulfilled a prophecy that he would end up killing his father and marrying his mother, thereby bringing disaster to his city and family.
Deterministic compatibilism would read this story as: yes, free will and fate (Lat. fatum, "destiny", i.e. a form of "divine determinism") can co-exist. Oedipus has free will, but despite all willed actions to avoid his fate, the gods play a cruel trick on him and his free will, though existing, is overruled by divine determinism (fate) in the end.
The Hard Determinism interpretation would be: Oedipus only has the illusion of free will, circumstances (e.g. his environment & character) created by the gods (pre)determine the limited range of illusionary free will choices.
You are reading it as a modern and not putting yourself in the shoes of an ancient. I love a little snippet from chesterton on paradoxes (see below). Always remember that when you posit the supernatural, as they did, many more things are possible in your worldview, including miracles. They held fate and free will to both exist as truths and to hell with the paradox, transcendental truth overrides consistency. You will see many contradictions on fate and free will when you read ancient greek literature, but if you remember that they hold these as transcendental truths as primary they override the contradictions.
"The ordinary man has always been sane because the ordinary man has always been a mystic. He has permitted the twilight. He has always had one foot in earth and the other in fairyland. He has always left himself free to doubt his gods; but (unlike the agnostic of to-day) free also to believe in them. He has always cared more for truth than for consistency. If he saw two truths that seemed to contradict each other, he would take the two truths and the contradiction along with them. His spiritual sight is stereoscopic, like his physical sight: he sees two different pictures at once and yet sees all the better for that. Thus he has always believed that there was such a thing as fate, but such a thing as free will also. Thus he believed that children were indeed the kingdom of heaven, but nevertheless ought to be obedient to the kingdom of earth. He admired youth because it was young and age because it was not. It is exactly this balance of apparent contradictions that has been the whole buoyancy of the healthy man. The whole secret of mysticism is this: that man can understand everything by the help of what he does not understand."