Freud is a very misunderstood thinker because we are left with the challenge of whether we are able to literally take him at his words or if there is more of an interpretative element to his work. I think that his understanding of Oedipus/ Electra might be one of those instances. I am not certain if there is a pervasive and underlying urge to eliminate the father figure to possess the maternal one. It is almost a self- defeating situation: If one disagrees, then the label of "repression" can be applied and it becomes an infinitely regressive cycle. Perhaps, where there can be some level of understanding lies in identifying the the underlying urges which might exist in our own psychological makeup. This forces us to better understand ourselves and who we are. What might be on the surface might not represent in totality who we in fact are. If we can understand that there might be other motivations to our actions, perhaps, this is where Freud can best be appreciated. In this light, his theories on the unconscious and the Oedipal conflict might have more relevance and resonance.
Rather than because he has an innate hatred for his father, Oedipus Rex strikes the charioteer who lurches over him at the crossroads, and he kills the old man in his tragic hubris, anger and arrogance:
...The old man saw me/And brought his double goad down upon my head/As I cam abrest./He was paid back, and more!/Swingin my club in this right hand I knocked him/Out of his car, and he rolled one the ground./I killed him./I killed them all....And I myself/Pronounced this malediction upon myself!
It is this flaw of pride that causes Oedipus to slay his father along with the charioteer. Had he harbored some innate wish to kill his father, Oedipus would not know (1)who he was in the first place, and (2) if he did recognize the man as his father, why would he want to kill the charioteer?
However, from "Oedipus Rex" there can be some credibility established with the concept of a male child's wishing to marry his mother since Oedipus does marry Jocasta, his mother. Still, Oedipus does not know that she is his mother, so can Oedipus be culpable of any incestual desires? It would seem that he is not. In Jocasta's case, an argument can be made for the Oedipal complex on her side since she becomes aware of Oedipus's origin and seeks to hide this information.
Finally, the question arises as to why Oedipus pursues the truth until it is revealed. If he truly desires his mother, why does he seek to know what has really happened with the baby and the shepherd?
It seems that Freud had found a catchy phrase and classic name for his theory--that is all.
Freud argues that Oedipus Rex continues to resonate with modern audiences because it deals with males' innate urge to have sex with their mother and hate their father.
I can't really know if there is such an urge or not. But it seems more plausible to me that the play is about whether people have self-determination or if their destinies are fated.
Even assuming that we do have the urges Freud says we do, it doesn't seem like a play about it would be that fascinating because it's not something we think about consciously.
By contrast, I think we do wonder how much we can influence our own destinies and how much we are just subject to luck, fate, destiny, whatever. So I would tend to argue that the play explores that idea rather than Freud's Oedipus Complex.
Freud's construction of "Oedipus Complex" from Sophocles's play may be tenable or untenable to different critics and readers, but the importance of the psychic structure of Oedipus can hardly be denied either in psychoanalysis (even in early Lacan) or in literary criticism. The mental state is based on Freud's idea of "infantile sexuality" and the idea that the beloved or the wife is a position that comes into a being as a result of the fundamental loss-- a separation of the child from its illusory dyad with its mother with the introduction of the third in the form of the father. The beloved/wife is a slot that repeats the maternal slot. The father's arrival in the scene leads to what Freud called "Castration Complex." One must understand that Freud was just using a literary example as a model to discuss a psychoanalytical matter and not trying to give us an interpretation of Sophocles's play-text.
Jacques Lacan declared "Oedipus Complex" as Freud's fantasy and went to underpin its patriarchal under-structure. Deleuze and Guattari in their path breaking book "Anti-Oedipus" castrated the Oedipal structure as colonial, patriarchal and a capitalist trope too!