Besides removing supposed temptations to idolatry, Islamic jihadists want to ruin the artifacts of non-Muslim civilizations because doing so testifies to the truth of Islam, as the Qur’an suggests that ruins are a sign of Allah’s punishment of those who rejected his truth:
Many were the Ways of Life that have passed away before you: travel through the earth, and see what was the end of those who rejected Truth. (Qur’an 3:137)
This is one of the foundations of the Islamic idea that pre-Islamic civilizations, and non-Islamic civilizations, are all jahiliyya — the society of unbelievers, which is worthless. Obviously this cuts against the idea of tourism of ancient sites and non-Muslim religious installations such as St. Catherine’s monastery. V. S. Naipaul encountered this attitude in his travels through Muslim countries. For many Muslims, he observed in Among the Believers, “The time before Islam is a time of blackness: that is part of Muslim theology. History has to serve theology.” Naipaul recounted that some Pakistani Muslims, far from valuing the nation’s renowned archaeological site at Mohenjo Daro, saw its ruins as a teaching opportunity for Islam, recommending that Qur’an 3:137 be posted there as a teaching tool.
Video thanks to Pamela Geller.