Why was Rome worried about the spread of Christianity?

Christianity was spread through the Roman Empire by the early followers of Jesus. Although saints Peter and Paul are said to have established the church in Rome, most of the early Christian communities were in the east: Alexandria in Egypt, as well as Antioch and Jerusalem. Christianity gained adherents among both Jews and non-Jews, bringing them together with a message of unity before God.
Because Christianity was so diffuse, and also illegal and therefore kept underground, it is hard to speak of a united “Christianity” in this period. A more accurate statement might be that there were “Christianities,” that is, various forms of Christianity, with different takes on the religion and its message. Gnostics, Montanists, Docetists, and others, debated about the true nature of Christ, salvation, and the life of a Christian. Still, several important Christian writers, called Fathers of the Church—men such as Tertullian, Justin Martyr, Clement of Alexandria, and Clement of Rome—helped define, in a broad sense, the doctrines of Christianity as they would be recognized in the future. Their writings also helped sway people to adopt Christianity. They were mostly opposed by the Roman authorities, who sought to suppress Christianity.