"How do you explain the fact that the apostles went their death rather than renounce their faith? People do not die for beliefs that they know are false so if the apostles knowingly went to their deaths they must have believed that Jesus was really resurrected. And it is unlikely they would all believe this unless they actually witnessed the risen Jesus. This provides good evidence for the resurrection because no other possibility adequately explains the apostles' faith and willingness to die for their beliefs."
The above statement represents a common apologetic argument in favor of the resurrection. I think anyone who uses this type of argument is either misinformed or is being deliberately deceptive. This is because the stories about the apostles' faith and their willingness to die for their faith are not facts that can be confirmed independent of the Jesus legend. The stories about the apostles are part of the same legend.
So Christians are citing one part of the legend as though it were a fact and then using this "fact" to prove that another part of the legend is true. It is the equivalent of arguing "We know that Hercules killed the Nemean Lion because he was seen wearing the pelt of the Nemean Lion, and how else would he have got that pelt unless he killed the lion?" A person making this type of argument is either misinformed or dishonest.
It's even worse in the case of Christianity because the evidence of the apostles' faith and martyrdom doesn't even come from the texts that Christians consider to be trustworthy. The only apostle whose death is recorded in the bible is James. According to the book of Acts, James was killed by Herod with a sword because Herod wanted to kill a Christian in order to please the Jews. There is no indication that James chose to die rather than renounce his faith and no indication that he would have even been given a chance to renounce his faith. For all of the other apostles (except John who is not believed to have been martyred), the accounts of their martyrdom come from sources that are even less trustworthy than the book of Acts. They are sources written much later (50 to 100 years after the canonical texts) and that contain wildly implausible miracle claims. These sources are dismissed by most Christians are fabrications, but they still want to maintain the belief that the apostles were willing martyrs. So rather than cite these discredited sources, Christians will simply cite "tradition."
If you ask Google how the apostles died you will get numerous Christian websites that tell you what happened to all the apostles, but none of them cite any sources. They will either just assert what happened without a source, or will cite tradition as the source. By this they mean that either some early church father made a martyrdom claim, or that the non-canonical texts are embellished accounts of widely held beliefs among early Christians.
So the sources that tell us the resurrection story are actually earlier closer in time to the event than the sources we have about the apostles' deaths. There is no good reason for someone to accept the martyrdom claims being real unless they already accept the resurrection claims. This means using the apologetic argument above with someone who doesn't already believe in the resurrection is either dishonest or misleading.
This could be disproven by citing some reasonable evidence for the apostles martyrdom and I invite you to do so if possible.