Well the answer is a somewhat varied one. one answer is because since the christian religion was so different from the roman one and because they constantly competed over followers they sorta declared war on each other. another reason is because Christians insisted roman gods didn't exist and that-in roman minds-was a major crime.
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Nero is said to have killed many Christians in Rome during the first century, as punishment for the Great Fire of Rome. On this, Richard Holland (Nero: The Man Behind the Myth) says the lack of an authentic and specific early Christian source for a mass persecution under Nero is very odd.
To throw further doubt on the numbers involved, the third-century Church Father, Origen, writing of the total of Christian martyrs up to his own time, in Rome and elsewhere (Contra Celsum, 3.8), states that there were not many - and that it was easy to count them.
So we can say that some Christians were indeed killed, but not nearly as many as later Christian tradition holds, and that such deaths as did take place included punishments for alleged wrongdoings and lack of allegiance to the empire.
Another answer from our community:
The Romans executed Christians because their beliefs were considered decadent and treasonous.
Punic Wars?
the Romans feed the christians to the lions and see this video named"Pompeii the last day" it is sad, and exciting, 50 minute video.
Nero was the emperor who fed to the lions, burned alive, and crucified Christians of the early church. He was also emperor when Rome burned to the ground.
The judaic influence of the early Jewish Christians: "God" built the world in six days, then he rested.
They used them because they wanted to kill them, eat them, regugitate them and mix it with medieval paint.