The idea that fate is absolutely unavoidable is central to the drama Oedipus Rex. When Sophocles wrote the play, most of the audience was already familiar with the basic story, which had been told in Greece for years. The value of the play was not so much finding out how the story would end (they already had a pretty good idea), but in watching the characters struggle against fate.
Specifically, Oedipus finds himself banished by his own decree when it turns out that he is the murderer of King Laius (who, unknown to Oedipus, was also his father). Although Oedipus had no idea that it was the king of Thebes he killed, he still has to pay the price when the truth comes out.
In our modern sense of justice, we would like to see Oedipus let off the hook. He did not intentionally do anything wrong. But fate, in the old Greek sense, is not necessarily just. The gods will get what they want. In this case, they want Oedipus removed from the throne and out of Thebes altogether. In the process, lives are destroyed and Oedipus is ruined.