To make it very simple: the Bible cannot and does not provide BCE dates or CE dates. This means that the WTS completely relies on secular sources for dates. The WTS accepts from secular sources the date of 539 BCE for the Fall of Babylon. These secular sources derive this date from a chronology that the WTS does not accept.
These sources say that the 37th year of Nebuchadnezzar is an Absolute Date that is fixed at 568 BCE. Then using the neo-Babylonian chronology these secular sources arrive at other dates, including 539 BCE.
BTW. Your father can feel comfortable communicating with me since I have never been associated with Jehoavh's Witnesses or with the Watchtower Society.
Doug