Mealtime for a creature that is half big cat and half big bird* must be confusing.
The cat part must be thinking "eat that bird head!"
Except that the bird head is the part that houses the brain, so the thinking is more like "don't let that cat body get us, escape!"
But the head requires that cat body for any escape movement.
So, the gryphon is like a hermaphrodite except with parts that repel rather than attract.
* Not half Sesame Street's "Big Bird," but half eagle, a large bird.
Gryphons wouldn't have lasted long if they were flying around with that big yellow friendly head.
And they're not around now.
So maybe that IS what happened.