For me it was discovering the Society's dishonesty in science-related things. It wasn't merely disagreeing with their interpretation of scientific observations, but finding that they so often misrepresented what scientists said. If they can't be honest in simple matters of quoting, which are easy to verify, then their interpretation might be out to lunch too. After doing lots of research on science topics, I found that their interpretations were ridiculous in many areas, even more so than their quoting practices.
As some readers know, I've written a detailed expose of the dishonest quoting and interpretation practices of the Society in regards to their 1985 Creation book. In the summer of 1997 I happened to be in New York, and so I took some time and went to Brooklyn Bethel to try to speak to the author of the book, one Harry Peloyan. Peloyan has been in the Writing Department for some 40 years, and happens also to be the chief editor of Awake! magazine. He came down to the lobby of the 25 Columbia Heights building (this is the one in which the Governing Body holds its official sessions every Wednesday) and we talked uneasily for about 45 minutes. He wasn't too happy about being confronted with my accusations of dishonest quoting practices, and mostly refused to discuss anything about it. But later in our discussion he allowed that perhaps one or two quotations might have been a bit off. As for the rest, he said, "Are the words quoted correct? Then that's all we need to worry about." I said, "That's not so. You have to make sure that you don't violate the author's intent. Otherwise you've misrepresented him." He didn't agree, so I said, "Ok, think of it this way: Suppose The Watchtower quoted an evolutionist who said, 'Evolution is true', and then I turned around and started telling people that the Society now says that 'evolution is true'. Would I be quoting The Watchtower fairly, even though the words I quoted were exactly correct?" He refused to answer. So I know that Peloyan and other WTS writers often know when they're being dishonest, or twisting statements to make them say different from the author's intent.
Once you discover that a religious authority is dishonest in relatively straightforward matters like science, you wonder about its honesty in religious matters such as interpreting the Bible, which are much more difficult to verify. Upon doing research in relatively straightforward matters such as the 607 question, and whether earthquakes and other disasters are far more common in the 20th century as the Society claims, I found exactly the same dishonesty as with science matters -- flat out misrepresentations of sources, marginal interpretations (excuses, really) of much material, generally poor argumentation, appeals to their own authority rather than to the facts, and so on.
When you discover that a religious authority you thought spoke for God is really a sham, you quit. At least, I would think that honest people would quit.
The 607 business is a classic example of the Society's using its own claimed spiritual authority to keep a teaching in place. JWs accept the WTS's version of "Bible chronology" because and only because the Society teaches it. If Brooklyn changed its mind today and acknowledged standard secular chronology, by next week the entire JW world would accept it too. Why? Because any JW who didn't would be disfellowshipped. So much for the intellectual honesty of Jehovah's Witnesses.
The problem is that the Society's leaders have really usurped the places of God and Jesus in the hearts of most JWs. By becoming the source of biblical interpretation, they have really become, in practice, God. Why? Because JWs in practice get all their information about God, and from 'God', from the Watchtower Society. This is because JWs who say that they accept their own interpretation of the Bible over the Society's are soon disfellowshipped for apostasy.
What all this results in is a form of the very nationalism that the Watchtower condemns: "my religion; may it always be in the right; but right or wrong, my religion". This is what I call The Fundamental Doctrine of Jehovah's Witnesses -- the emotionally based belief that Watchtower leaders directly speak for God, and no matter what facts get in the way, must be treated as God's special prophets.
AlanF