Bullet point review 
*It is certainly true that Christians should be credited for coining the term martyr as we now use it. It doesnt seem to have been the case for ancient Jews, Greeks or Romans had their own technical terms for people who died for their religious beliefs. They were heros who died good deaths. In creating terminology to describe people who died for Jesus, Christians were doing something new. It is tied to the fact that Christians acted as legal witnesses and were subsequently sentenced in actual courtrooms.
*Socrates has been called by some as the "world's first recorded martyr" and  his manor of embracing death for  principle provided a model for subsequent generations  of well educated Greeks and Romans.
*Greeks and Romans wrote extensively about glory of dying for a cause. This can also be found in Hebrew scriptures' and in ancient Jew literature.  Hints of this idea can be found earlier, the idealization of dying for a God or the law really began to take shape in the second century CE, when Jews lived under foreign rule.
*From the very beginning Christian authors used the death of others, non Christian heroes, to tell their own stories. To this day millions of Christians appeal to the example set by Jesus as a guideline for their ethical conduct. Protestants ask themselves "What would Jesus do?" but the problem with that is what Christians received in the Gospel of Luke, the model embodied by Jesus was itself partly based on non Christian examples.
*The distinctiveness and simplicity of the writing style has led many scholars to argue that these Christian martyrdom accounts were based on actual court documents. They are transcripts of what actually happened in the court room. This scholarly position is incompatible with the view that Christians created their own new genre. It cannot be the case that an early Christian style martyrdom account is both a copy of a historically accurate authentic court transcript and a completely new Christian genre. Either they are copies of court documents or they are a whole new genre. The earliest Christina accounts of martyrdom are concerned exclusively with what took place in the courtroom.
*Even a brief story of Christian martyrdom were influenced by the Romans and Greeks and even the Jewish traditions about death. The heroes of the classical world were reshaped into soldiers for Christ. Christians are thought to be unique because they die for Christ but the stories on which they communicated their uniqueness are borrowed from other cultures.
*The legend would have us believe that the Romans were constantly and continually persecuting's Christians.  The martyrdom myth would have us believe that Christians were constantly persecuted and died in huge numbers.  Instead of Romans persecuting Christians, Christians were actually volunteering to die.
*If the Roman emperors had a problem with Christians and Christianity, it was because they threatened the stability of the empire and appeared to make divisive political claims. Roman emperors had problems with those aspects of Christianity  that sounded like treason or revolution.
*Roman judges weren't entirely sure why Christians wouldn't participate in the imperial cult. Christians rejected the imperial cult and military service as well. Roman pacifism did not exist as a concept. It was a pattern of Christian behavior that resisted, seemingly for no good reason, that was confusing and strange.
*The Romans rarely persecuted Christians and when they did they had logical reasons that made sense to ancient Romans. Christians posed a threat to the security of the empire.