Because someone, anyone, even your Dad, told you, does not answer the question.
WHY? If there isn't a valid reason for something, it may not be accurate. Perhaps, for his body type, gripping in the middle of the wrap was correct, but that doesn't automatically make it correct for you. Maybe someone told him years ago that was how to do it, because that was how they did it.
Again I ask the simple question. WHY should you grip the cue in the middle of the wrap? Is there a physiological reason that this is the best position? If not, you may need to reconsider the idea.
In pool school, we always ask our students to forget everything they think they know about shooting pool for a couple of days. The only way to learn is to have an open mind. Open up to new possibilities. If you continue to do the same things the same way, you will get the same results. In order to improve, you have to be willing to consider change.
You posed a question in the original post that suggested you were looking for ways to improve. Improvement comes from trying new and different things.
BTW, I used to always hold my cue at the wrap. Since I have learned how to stroke properly, my grip hand is now down on the butt cap.
Steve