Oedipus believed that kicking laius chariot off the road was justice. He didn’t keep it a secret that he kicked the chariot off the road. He thought that since they are blocking my way and I need to get through the only thing to do is kick their chariot off the road. Oedipus didn’t think that what he was doing was a crime. He didn’t think twice about it because it was justice in his eyes.
Oedipus also didn’t believe that death was a good punishment. He believed that the correct punishment for the murderer of laius was exile. If he killed them there would be no real punishment because they wouldn’t have to face the crime.