The young, bold Bellerophon dreamed of taming and riding Pegasus, a creature who had been ridden by no one.
Athena gifted him a golden bridle after he slept in her temple, and he successfully mastered Bellerophon, aided by the Winged horse, he quickly became unbeatable.
At some point, Bellerophon wound up murdering his brother, leading to him meeting king proetus to be purified. However, his wife, anteia, fell in love with him, and when he would not reciprocate it, she grew angry and demanded her husband kill him.
Convention prevented proetus from killing him directly, so he sent him to king Lycia with a note telling him to kill Bellerophon, however, the same convention kept him from killing him directly, so he asked Bellerophon to kill the chimaera, thinking he would fail. However, with Pegasus aiding him, he safely shot the chimaera and returned to proetus.
Proetus tried killing him by sending him to the solymi and Amazons, but he survived both encounters.
Eventually, Bellerophon was consumed by arrogance and attempted to ride Pegasus to Olympus; however, the wise horse bucked him off, leaving Bellerophon to traverse the world without wings and with plenty of anger to spare. Pegasus, ever loyal, found shelter in the stalls of Olympus.
Bellerophon is a powerful, intelligent hero. Working with Pegasus, he was essentially unstoppable, and took on tasks with great courage, revealing a Greek emphasis on courage.
However, his arrogance was his downfall. His desire to fly to Olympus led to his getting separated from Pegasus, leaving him to wallow in anger for the rest of his life. This exemplifies the Greek value of humility.
The myth of Bellerophon and Pegasus mainly reveals the innate human desire for power. BELLEROPHON’S craving for power led to him seeking out Pegasus in the first place, and ultimately his futile attempt to fly to Olympus.
This also demonstrates that though seeking power isn’t inherently bad, as seen in the former case, allowing it to cloud your judgement can be dangerous, as seen in the latter case.