Seems the moral here is that humans already have a common internal mechanism for overturning belief systems that has nothing to do with rationality: outlining it completely would take me more research and probably enough space for a top-level post (it hasn't been addressed directly as far as I can tell), but it's related to the cult attractor and you can see suggestions of how it works in conditions like Stockholm syndrome.
Being a lot more common over the set of all humans than having accurate intuitive access to a truly rational procedure for deciding between elements of belief systems, it makes sense to consider it a more likely cause for your own decisions in the absence of evidence for such a decision procedure.
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).