Why didn't Tiger Woods "own up" from the beginning?

It's called damage control. Think about it we would all try to "own up" to as little as possible. Remember when you were a Kid and your parents caught you doing something you were not supposed to be doing. You did the same thing... gave them as little information as possible to not get yourself in more hot water and in hopes that it will all go away. Realistically, once they took their fight outside their home and got into a situation (car crash) that drew attention to them, Whatever happened afterward, probably could not have happened any other way.