Furthermore, how would a professional historian go about investigating such a broad, general claim? Is it possible to even answer the question?
The aforementioned teacher pointed to the Greek myths- in particular, the major role of destiny or fate therein- to justify his claim. He stated that the concept of free will arose in order to justify the concept of hell.
That's a strange claim! Stoicism for instance grappled with the concepts of free will and fate, and tried to manage the tension between the two: you can see this in both Marcus Aurelius and the more technical Stoical writings. For that matter, many Christians believed and believe in predestination and, much like the stoics, have to square that concept with free will. Epicurus made some room for free will in his materialist account of the world by including the idea that sometimes atoms 'swerve' and Lucretius was even clearer that this meant people's own decisions matter (rather than 'swerves' being random)
It's true that fate (Tyche/Fortuna) is important in the Greco-Roman world. But I'm not sure where the idea would come from that free will was 'invented' by Christianity.
As for justifying hell: the Christian concept of the afterlife was starker than many others, but it's not as if hell was created from whole cloth. The Aeneid includes a depiction of suffering in Tartarus, for instance.