Oedipus Rex and The Big Q

In Oedipus Rex, Oedipus discovers that his oracle states that we will end up killing his father. In order to avoid killing his father he leaves his family behind and starts his life somewhere else. Along the way to his new life, he meets a carriage on the same road he was on. They were coming towards each other and Oedipus did not want to move, so he killed the man in the other carriage. Most people would consider this to be morally wrong, but Oedipus does not seem to have a problem with it. He is worried about killing his father, but is okay with killing a random person? This just doesn't seem right to me...