While, nobody's really sure why the Fallen think this. It could be that they somehow blame us for the Great Machine disappearing during the Whirlwind (essentially their version of the collapse), or that they just think that it rightfully belongs to them. However, another theory is that, in the days immediately preceding the collapse, the Fallen attempted to get to the Traveler, and some humans fired on them, setting off the war. In any case, all the Fallen seem to care about is the fact that we have the Traveler, and they don't.