The Qu'ran tells Muslims that the world is divided into:
It specifically orders Muslims to conquer Dar al-Harb lands by various means, including infiltrating them in small numbers, acting weak (taqiyya - deception of infidels), then using breeding rates to grow the numbers up. Once the numbers are up, the real violence and terror begins. Civil unrest, finally civil war and extermination of the non-Muslims. Much of the Islamic world never used to be Islamic, they have used this method successfully time and time again.
TL;DR: They are here because they want YOUR lands. They believe it is a holy mission to conquer you and your lands. They have no intention of fucking off, because it is an invasion and conquest.