'You go back to kill your father, but you'd arrive after he'd left the room, you wouldn't find him, or you'd change your mind,' said Professor Greenberger.
I would take that one step further. The series of probabilities that led to your father being born are practically infinite. If you could go back in time, you'd just find yourself in a pretty strange place, and most definitely a different history than what you knew of in the present. And no chance of running into anyone that you know.