The secular date of 587 BCE is for the most part deduced from available archaeological findings. While ancient commercial cuneiform documents, inscriptions, and king lists provide some definitive information, when these disagree with the Bible's chronology, we choose to rely on the inspired Word of God.
This is classic brain's in backwards thinking. The logic should be, if the majority of other ancient documents contradict your ancient document then your ancient document is probably wrong.
The cold fact is that proving that the bible is the infallible word of god is only possible if you start with the assumption that it IS the infallible word of god.