The myth of Arachne is one I can remember reading about in elementary school. It's apparently one of the later Greco-Roman myths to develop, and appears to have been found exclusively in Roman sources. Arachne was a weaver who lived in Maeonia in Lydia, whose skill was legendary, and who bragged that she was even better at it than the goddess Athena. In order to settle this, the goddess agreed to participate in a weaving contest with Arachne. Athena's tapestry portrayed both her competition with Poseidon for the city of Athens and scenes of mortals being punished for their pride, while Arachne chose to focus on the infidelities of the gods. While the myth never seems to identify an actual winner, Athena was jealous of Arachne's work, and tore up her tapestry and instilled her with a sense of guilt. This led Arachne to hang herself, but the goddess brought her back to life as a spider.
What's the lesson to be learned from this story? Well, the myth-makers would probably have said it was a message not to be done in by hubris, and to remain humble before the gods. But Arachne really WAS pretty much the equal of Athena as far as weaving was concerned. So the myth actually suggests that mortals can be just as skilled as the gods at certain tasks when competing on a level playing field. It's just that the gods are sore losers, and prone to cheating. It's not that you shouldn't brag because there's always someone better than you, but rather because someone else might get pissed off and turn you into a spider. It's sort of like how Jacob wrestled with God, and God had to dislocate the patriarch's hip because He just couldn't overpower the guy. I guess it's not that humans can't beat the gods, but that the gods just don't take well to it.