The parent would not be directly responsible for his death and in this way could live his life feeling less guilty. In Jocasta's case, when she abandons her child, he feels guilty, therefore, after she becomes suspicious of the prophecies, his guilt grows. In the time that Oedipus the King is set, people have a lot of faith in gods, destiny, and prophecies. It was therefore imperative not to anger the god or do anything that might dishonor you or your family and not be allowed into heaven. It is important to recognize that while Jocasta is suspicious of the prophecy, it is not completely sacrilegious, and even in the story we read of her praying to Apollo. By praying to Apollo, she makes offerings and asks him for protection. No one other than the Choir goes as far as Jocasta when it comes to prayer. In many ways, she could be characterized as one of the most God-fearing characters in the play. Not that his blind devotion does him any good in the long run. It's really not the god that Jocasta tires of, it's that they are meant to be servants like oracles. I threw away the coin you find.