Is to betray us, and destroy the city?
TIRESIAS: I will not bring remorse upon myself
And upon you. Why do you search these matters?
Vain! Vain! I will not tell you. (Rex, 12-13)
OEDIPUS: Nay, it cannot be
Thant having such a clue I should refuse
To solve the mystery of my parentage!
JOCASTA: For Heaven's sake, if you care for your own life,
Don't seek it! I am sick, and that's enough! (Rex, 38)
OLD MAN: Don't, master, for God's sake, don't ask me more!
OEDIPUS: You are a dead man, if I speak again! (Rex, 41)
Obviously, everybody doesn't want the king to know what he's done to his parents, for they believe that he will react in the worst possible way to it. And they're right, of course - As the old saying goes, curiosity blinded the king. Or, something like that.
Speaking of blindness - Oedipus's eventual actions could be a symbol of the fact that he was blind throughout most of his life - Blind to truth for most of the book, and then blind of sight afterwards. Basically, when he saw, he became blind. Actually, blindness does pop up a great deal in the book - Tiresias is also blind, yet he's one of the first to know the truth. In fact, at times it seems like every character in the book is blind in a way, and yet also sees.
The final theme that I'm going to talk about is fate. Of course, fate was a far bigger deal in Greece than it is today, and a lot of Greek tragedies tackle this subject: How a person knows what their eventual fate is, and will do anything to attempt to stop it:
OEDIPUS: Did she then give it you?
OLD MAN: My lord, even so.
OEDIPUS: For what?
OLD MAN: For me to make away with [The baby].
OEDIPUS: Herself the mother? miserable!
OLD MAN: In dread
Of evil prophecies-
OEDIPUS: What prophecies?
OLD MAN: That he should kill his parents, it was said. (Rex, 42)
So, if we are to believe that fate planned out this entire story, then Jocasta was fated to attempt to kill Oedipus. By attempting to stop fate, she acted exactly according to plan.
Or perhaps, the only thing that was fated to happen was that Oedipus was to kill his parents; Perhaps it wouldn't matter how it happened, just so long as it happened. Perhaps by tempting fate, Jocasta not only allowed herself and her husband to be killed, but also ended up sleeping with her son. Perhaps Oedipus's parent's could've died in a way that was equally tragic, but would've at least involved less incest if the mother hadn't attempted to rewrite her destiny.