Why is Latin the liturgical language if the Romans persecuted the Christians?
Greek was the common language of the Church for the first three centuries (during the period of most of the persecutions). During the third century Latin became the common language of the Western Fathers. It was also the common language (as opposed to official language) of the people of Rome. From that usage the Church in the West used it as well. The common use of Latin among the educated people in the West spread through the 7th century and, as a consequence, became the official language of the Church.