Oedipus's attempt to avoid his fate only leads him further into his destruction. All of his efforts to try and save himself from his fate were in vain. To kill his father and marry his mother is his fate, and fate cannot be fought or avoided. It will become true whether we are aware of it or not. All of the efforts we do to try and prevent our fate from coming to be are futile and will only lead us further into what we wanted to avoid in the first place. However, we still can be happy if we ignore this fact. As long as we keep ourselves disillusioned in a false reality, we can be satisfied with our lives. In Oedipus's case, we see his tragic flaw progressing his path to doom.
We cannot run from our fates, nor can we avoid our destiny. The Delphic Oracles prophecies were final. Jocasta and Laius attempted to challenge this prophecy by exposing their son on a mountain, but their attempt was in vain. There was of course a way that fate managed to get around the obstacle. The Shepard found adoptive parents for the baby, and from that moment on, Oedipus starts to drive himself into the path of destruction.
Once Oedipus learns of the prophesy that he ill kill his father and marry his mother, he is determined to do everything inn his power to avoid it. Oedipus tries to design his own fate, which is to avoid the true one. However, almost all of his actions just take him one step further into the path of destruction. The very first step he takes is to leave Corinth and move as far away from his "parents" as possible. In reality, by moving farther away from his adoptive parents, just brings him closer to his real ones.
Oedipus encounters Laius on the road and kills him, thinking that he has saved himself from a potential robber. He is unaware that half the prophecy has now been fulfilled. In the process of Oedipus's attempt to flee his parents and his destiny, he accomplishes one of then and within seconds the prophecy is fulfilled.
