The trick about 607 BC is first to acknowledge that the date is not mentioned in Scripture, in fact no date according to our calendar is so mentioned. The reason is because the people in Bible times had a different dating system to ours. We simply have to deal with what is supplied by the text and to transcribe that to our modern dating system.
Instead of saying either in 607 BC or in 586 BC...etc, what the Bible does say is: "In the nineteenth year of Nebuchadnezzar ...." [2 Kings 28:8] So the question arises: When was this 19th year?
Well, there are two schools of thought.
On the one hand there is the entire body of scholarship from every single university and scholastic institution in the world, which says 586/587 BC [Dont be too concerned about that forward slash. That's because the Bible uses two dating systems called regnal and succession years, and we aren't sure which the Bible is using at the text of 2 Kings 25:8, but the difference is only that of six months] and then there is the Watchtower, which says 607 BC. Why this stubborn inclination to hold on to this discredited date? Because this date conveniently leads to 1914 AD, a date pivotal for current Watchtower theology. When the Watchtower drops 1914, they will drop 607 BC. Betcha.
How can you tell which is the right date? Well, again there is no simple 6 second sound bite, like on TV where we can say one way or other. It takes some thinking and calculation. First, the time period we are talking about is called the Neo-Babylonian period. If you looked up Doug Mason's site that he refers to above, you will see that he lists, according to the historical information available to all, the 5 kings who made up this period. They reigned for a total of 66 years [count 'em] ending in 539 BC.
Now if this period ended in 539 BC, which is a year that the Watchtower agrees to, then when did this period begin? All you have to do is add 66 to 539, which leads to 605 BC. That means that this Neo-Babylonian period began in 605 BC which is the year that Nebuchadnezzar became king.
If 605 BC was his first year then when would his nineteenth year be? Again just count back 19 years: 604, 603, 602, 601, 600, 599, 598, 597, 596, 595, 594, 593, 592, 591, 590, 589, 588, 587 586 BC. Got it? It is so simple and so enlightening that even a child should be able to grasp it.
The Watchtower on the other hand resorts to subterfuge, obfuscation, prevarication, discrediting, circular rationalization, assumed illogic, retrograde cognition, [which is also called "proving that which is assumed". If you assume something you can easily "prove" it. Even a flat earth.] and other fallacious forms of so called "reasoning".
They also use pious platitudes along with imperious pontifications to try and hijack the subject. They will use buzz words like "But evidently this"...and "evidently that" As Deut 18:22 says of false prophets [who make unjust profits]: You must not fear such men!