The apostles choosing death over renouncing Jesus is a popular meme, but we don't actually have a historical basis for supposing that it happened.
As Richard Carrier notes, of the little evidence we have for early Christian martyrdom, none of it was as a choice between recanting a belief in Jesus and dying. They were simply killed on trumped up legal charges from which recanting would not have saved them.
Certainly there have been people who have chosen to die rather than recant their beliefs, in plenty of different religions. It wouldn't even be particularly strange if early Christians did so, and it's certainly possible that it happened, although it would not be significant as evidence for Christianity, for reasons that others have already addressed. But it appears that all our stories of this actually happening to any of the apostles were simply made up somewhere along the line by people who were in no position to know.
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).