In The Winter's Tale, why did Leontes refuse to believe the Oracle's words?
The simplest answer to your question is that Leontes is in self-destruct mode. His jealousy and irrational thirst for revenge are so taken over, that it is impossible for him to hear even an impartial Oracle as reasoning against what he has already decided -- his wife, Hermione, has committed adultery with his best friend and given birth to a bastard daughter. Both, in his mind, should be put to death. Oh, and that probably means that their older child is not his son either, so should also be put to death. This is not the thinking of a rational man looking for rational answers.
Shakespeare is setting up Leontes to act in the most egregious manner possible in these early scenes, so that the redemption and rebirth he experiences at the end of the play can have the most miraculous tone possible. He must experience the lowest of the low in behaviour in order to be granted the most undeserved grace of restoration at the end.
So, it is consistent with this structure in the story (as well as suiting his out-of-control-with-jealousy behaviour) that he will not even listen to the objective counsel of the Oracle.