The problem with analyzing much of Greek mythology using the 12 steps of the Hero's Journey is that many of the myths are sans hero. Sans is French for "without." Why didn't we just say, "without?" Because we like it when you learn things. Anyway, the point is that without a hero you can't really have a "hero's journey," can you?
Take Minerva and Arachne, for instance. If we begin with the idea that Arachne is the hero we're forced to realize that she doesn't
- go on a journey (either physical or spiritual),
- consult with or learn from a mentor,
- recruit friends or allies,
- obtain any kind of reward,
- or return home triumphant.
Arachne does face death and rebirth, which is a mark of the hero's story, but she does so in a totally unheroic way. She commits suicide and is then resurrected before becoming a spider. Add to this the fact her characters comes across as self-absorbed, angry, and annoying, and we're forced to conclude that Arachne can't be the hero of the story.
What about Minerva, then? Maybe she's the hero? Well, Minerva does:
- receive a call to adventure (in the form of the rumor she hears),
- go on a journey,
- cross a threshold (into the mortal world, or into Arachne's house, whichever),
- face her worst fear (that Arachne might actually be a better weaver),
- and obtain a reward (in the form of killing her adversary).
From here it looks like Minerva actually could be the hero. Maybe we should back up and follow all 12 steps. But wait; let's look back at Minerva's motives. Jealousy, anger, frustration, fear, pride; are these motives of a hero? Minerva beats Arachne to death with a wooden shuttle because she can't face the idea that Arachne might be a better weaver. This clearly isn't the sort of thing a hero does. Sadly, we have to recognize that Minerva can't be the hero either.
So while many of the twelve steps are present in the story, we don't have a hero to follow them. What we have is a collection of events that halfway fit, if we wiggle them back and forth enough. Rather than trying to force everything into place it's more helpful to realize that not every myth is a hero myth. Then we can step back and ask "what parts of the hero's journey fit into other types of myths, and why?" Now that is a great question.