It is often claimed by Christians that the apostles of Jesus were martyred for their beliefs and because they did not recant, they truly believed what they were preaching, that is to say - they were not making it up, they did not lie.
There are a number of problems with this claim
1) There is very little evidence that Jesus' apostles were martyred.
2) If they were killed, we may not know why they were killed.
3) If we knew why they were killed, this doesn't tell us about which belief they died for.
4) There are numerous parallels with other people dying for their beliefs.
5) All we are left with is the impression that they really believed something, but that does not make it a physical reality.
There is very little evidence that Jesus' apostles were martyred.
It is generally accepted that the stories of Jesus' apostles being martyred are "traditions" with a few exceptions. Some of these traditions contradict each other with some apostles being killed in different locations. Many traditions only start to appear in the written record hundreds of years after the events with no contemporary or near contemporary accounts. This makes the reliability of the traditions suspect. Many Christians parrot these claims without understanding the lack of evidence for this belief and if they are to use it as an argument in favour of their belief, they are merely repeating legends thought up to make Christians feel good about being persecuted.
If they were killed, we may not know why they were killed.
Let us presume for the moment that some early Christians were killed of their beliefs. We may not know the circumstances behind their arrest, trial and execution. Christians were persecuted for going against Jewish and Roman laws and customs. We do not know if they had any opportunity to recant their beliefs before being killed. To say they were martyred for going against the laws of the land does in no way bolster the validity of their belief than does a political protester.
If we knew why they were killed, this doesn't tell us about what belief they died for.
Let us presume that they were killed for preaching Christianity. This doesn't tell us which version of Christianity they died for. Were they preaching a bodily risen Jesus as represented in the gospels and orthodox Christianity, or were they preaching a non-bodily risen Jesus as implied in the letters of Paul, or perhaps they were Gnostic's? For all we know they could have died preaching something which is completely different to what modern Christians now believe. This would render their death in vain and would give no validity to orthodox Christianity.
There are numerous parallels with other people dying for their beliefs.
Joseph Smith, the founder of Mormonism was persecuted for his beliefs yet did not recant. Does that mean he was telling the truth? (I'm sure most Christians agree that he was a false prophet, some even believe he was intentionally dishonest) We also know people are willing to die for their beliefs about being abducted by UFOs. In most cases I have no doubt people really truly believe what they are spouting, but this gives no validity to the truth claims behind this belief.
All we are left with is the impression that they really believed something, but that does not make it a physical reality.
We know modern Catholics believe Jesus is really present in the Eucharist, yet there is no physical evidence this is the case. Given that, would a Catholic who is willing to die for their belief in the presence of Jesus in the Eucharist lend validity to the actual presence of Jesus in the Eucharist? In fact, if an aspect of a religion requires faith, even faith in things believed but not seen, then we should expect that there are devout people who are willing to die, an ultimate test of their faith, which wouldn't be too much of an ordeal considering they are promised heaven on the other side.
Given the lack of evidence we have, we ought to be sceptical of the claims that Jesus' Apostles died for their belief in the physical resurrection of Jesus. As arguments for the validity of Jesus' resurrection go, this argument is one of the least arguments I find convincing - firstly because there is little foundation in evidence and secondly because it doesn't reveal to us anything other than establishing that they believed what they preached - which many people do not doubt. (Which would technically render this argument a straw man because people don't really believe they were liars)