Oedipus' culpability lay in his thinking that he could outdistance fate. The problem was his inconsistent problem solving. He took bold action in some regards, and was sloppy in most other areas in which caution was needed.
It was foretold that subsequent Theban King Oedipus would kill his own father and marry his own mother. He thought that he could escape such a horrific fate by running away from home. But unbeknownst to him, he was running away from his adoptive/foster family, not his biological parents.
The ploy was effective in removing him from the domestic scene. But it wasn't the particular domestic scene that he needed to avoid. Additionally, he needed to be vigilant. He needed to keep his guard up and look every gift horse in the mouth. Specifically, he needed to avoid any violent interactions with individuals old enough to be his father. He also needed to avoid any romantic attachments with individuals old enough to be his mother.