This 607BCE vs 587BCE is an old discussion. However, you asked about why the Bible and this secular chronology does not match well. Here are the key points I had to focus on during my research.
1. Josephus in Ant. 11.1.1 clearly dates a 70-year desolation period beginning a "servitude" of the poor people who were deported during the last deportation in the 23rd year of Nebuchadnezzar. This is a critical reference since Josephus' view on this would reflect his interpretation of the Biblical reference here. In fact, he mentions this is how Jeremiah's prophecy was fulfilled. Here's the quote:
[Q]ANT 11.1.1
IN the first year of the reign of Cyrus 1 which was the seventieth from the day that our people were removed out of their own land into Babylon, God commiserated the captivity and calamity of these poor people, according as he had foretold to them by Jeremiah the prophet, before the destruction of the city, that after they had served Nebuchadnezzar and his posterity, and after they had undergone that servitude seventy years, he would restore them again to the land of their fathers, and they should build their temple, and enjoy their ancient prosperity.[/Q]
Mind you, this is not a Biblical quote, but is consistent with Scripture if you begin the 70-year "sabbath rest" period with the last deportation in the 23rd of Nebuchadnezzar which the scriptures definitely support.
But at this point your inquiry ends because there is no way possible to reconcile this since secular history's dating of the fall of Jerusalem in 587BCE and the 1st of Cyrus around 538BCE does not allow enough time for 70 years to elaspe after the 23rd year of Nebuchadnezzar.
Therefore, all the arguments are whether or not to accept the Judeo-Biblical dating for this period which involves an extended Neo-Babylonian period beyond that of secular historians.
That's the BASIC problem, even though many argue on side tangents. But the bottom line is that the Jews do ascribe a 70-year desolation period after the 23rd year of Nebuchadnezzar and that cannot be accmmodated by current secular chronology.
607BCE is a variation on many of the arguments regarding this period of time, with the witnesses using 2 Chronicles 36 as a definite reference to a 70-year period of time for the "land to keep pay back it's sabbath" and they add this 70 years to 537BCE, the date they have settled on for the return of the Jews from Babylon. The extended 70 years post destruction of Jerusalem is the primary contradiction as far as 607BCE vs 587BCE.
LG