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.

That may be what the majority does, but history is filled with people willing to die for their beliefs. From the Maccabees against Assyrian Greeks to Falun Gong against modern China, martyrdom is not all that historically unusual. And the beliefs supporting martyrdom are so blatantly contradictory that they can't all be right.

Moreover, martyrdom is not particularly Christian. For example, Rabbi Akiva was a great Jewish martyr.

This argument is fallacious and does not address historicity in any way. People throughout history have, in fact, died for beliefs which turned out to be false, deceptive, or poorly understood; such as suicide bombers being rewarded with virgins. Just because these men so firmly believed that their beliefs were true that they were willing to die for them does not give their beliefs any credibility. Here is an extensive list of refutations to this terrible argument.

Even this is making the generous assumption that the martyrs in question even existed. Some martyr-stories are known to be completely fabricated; the hagiography of St. Catherine of Alexandria, for example, is a partial rip-off of the story of Hypatia of Alexandria, the pagan philosopher who was skinned to death with tiles (by Christians!).

Yet they all went to their deaths. That doesn't impress you?

Not particularly.