In some versions of the tale, it is told that Athene was jealous of Medusa's hair, and so cursed her.It was Athena who transformed Medusa into a Gorgon. According to Ovid's Metamorphoses, Poseidon and Medusa's offspring was winged because the sea-king had assumed the form of a bird in order to rape Medusa. According to the Dictionary of Greek and Roman Biography and Mythology, some other ancient writer says that Poseidon took on the guise of a horse in order to commit the crime. It's the same reason the Oceanid Philyra gave birth to a Centaur: she and the Centaur's father the Titan Kronos had assumed the form of horses when the Centaur Kheiron [Cheiron, or Chiron] was conceived.
So does that mean that Poseidon took the form of a fish in order to rape some other poor woman, spawning the mer people? And some other god took the form of a lion or eagle to then rape the other for the griffin? Or a goddess who had taken on the form of the other animal? I'm not sure which I would prefer.