Muslims who commit acts of violence and terror in the name of God, can find ample justification for their actions, based on the teachings of the Qur'an and the sayings and examples from prophet Muhammad himself. Furthermore, the only sure guarantee of salvation in Islam is dying in Jihad. But other factors are at work:
1. Fundamental Islamic education has an effect on the attitudes of many Muslims toward Christians and nations they perceive as "Christian." They are told that Christians hate them and want to wipe Islam off the face of the earth and that they can never be friends unless they convert to Christianity (Surah 5:51-Ali Translation).
Additionally they are told great stories about heroes of the Islamic faith, like Khalid ibn Walid the "Sword of Allah" and taught an idealized version of early Islam when Muslims read the Quran literally and applied it to their lives. This, despite its bloody history. They learn songs like "I Shall Avenge My God and Belief" which tell of "delivering death and hell to the unbelievers." It's important to note that the modern Great Awakening of Islamic fundamentalism we see today is based primarily on the modern society defined as Jahiliyyah and the "need" for a vanguard to re-Islamize society.
2. Islamic law. One point that separates the radical Muslim from all others is Islamic law. Islamic law is a powerful concept because it is viewed as a direct command from the Quran. Radical scholars attach it inseparably to the worship of Allah. Islamic law is the line that divides the religious terrorist from the secular terrorist. It's rigid logic binds the radical Muslim to Islamic law with resolve.
3. The radical sees themselves as surrounded by infidels who are hostile to them and their message of faith. All key radical writers put great energy into arguing that nearly all societies are infidel both those who call themselves Muslim and the others. It goes without saying that Jews and Christians are infidels despite liberal attempts to show they are not because a small level of tolerance was afforded them as "people of the book"; a people to be certain whose numbers have dwindled after centuries of persecution and discrimination of a level few Westerners understand. The radical believes that Islam is not merely belief that should be preached but a way of life that must take shape as a system of authority on earth just as it did during the life of Muhammad. Islam is a theocracy: a religion and a state without borders.
4. Punishment or reward. The Quran condemned Muslims who avoided the duty of jihad (Surah 9:38-39, Shakir Translation) and in this religion that offers little guarantees in the way of eternal security, the Quran teaches that being killed in jihad guarantees one entrance to paradise (Surah 4:74). Moderates argue this is not primarily a physical fight but radicals always push back against those teachings.
There is no "new testament" in Islam. It's rooted in ancient violence.
Good article:
Islam and Violence