It is useful to begin by thinking about the opportunity cost of taking a compulsory philosophy class. What else could one do with the time? It is certainly arguable that liberal arts students should all be scientifically literate, or that they should have a grasp of world history and literature. There are many other subjects in which a survey class would appear to be merited. What are the special claims of philosophy?
To begin with, philosophy goes to the root of civilization in Western culture (and in others too, including Chinese culture). In Ancient Greece, teaching of any kind involved teaching philosophy. Socrates taught Plato. Aristotle taught Alexander the Great. At its most basic, philosophy involves teaching the student how (not what) to think. It has been defined as "a peculiarly determined attempt to think clearly," and this applies to thinking about science, history, literature, or anything else.
Socrates and Descartes question the possibility of knowing anything at all. Socrates said that true wisdom was to recognize that one knew nothing. Descartes said that when he began to take philosophy seriously, he dedicated himself to the destruction of all his former opinions, so that he could work out if a priori knowledge were even possible.
Philosophy examines the biggest questions it is possible to ask. Is knowledge possible? Does life have meaning? How ought one to live? Is there a God? On this last question, even Richard Dawkins, perhaps the most famous atheist in the world, has said that he would have been a Christian if he had lived before Darwin. However, philosophers who lived before Darwin, including David Hume, wrote cogently and persuasively about their logical objections to the existence of God. To study philosophy is to engage with the greatest minds on the most important subjects. This point alone is ample justification for liberal arts students to be required to take a philosophy class.