Humanities programs have sometimes been criticized as promoting a superficial knowledge of many things, and little or no means of systematically studying anything. This criticism does, in fact, have some legitimacy for some humanities programs in the past. Many have been surveys of a host of different fields, and have merely sampled small aspects of those fields.
One assumption behind this is that specialization is better, that it is more likely to create knowledge (or in the case of education, more likely to produce well educated students). Certainly specialization is important - I wouldn't want to go to a doctor who just had a smattering of knowledge about medicine, along with lots of other stuff. And yet, I would want that doctor to know other stuff as well. A doctor who has done nothing but study diagnostic and surgical techniques may well forget that he/she is dealing with actual people. There are lots of stories about doctors treating people as if they are just problems to be solved, rather than people with complex lives.
In other words, specialization is essential for many things, including the study of the humanities, but any study happens within a larger context. To use the example of medicine for awhile longer, people have begun to realize that we are not just like machines, with causes and effects. We are integrated into our environments. We are not even just reducible to our genome - there is a very complex relationship between ourselves and our genes. It is rare that you can find a pill for a specific thing, or a gene for a specific thing.
Now, what about the humanities themselves. Certainly if you took the Humanistic Traditions courses at UCF, or their equivalent somewhere else, you might get the idea that we learn a little bit about a whole lot. Those courses are adequate as introductions, but they are of limited use as you go on in the humanities. We need those kinds of introductions, but we later we need to show students how to think about complex humanistic questions, using a variety of tools, and do so in a way that does not just yield superficial knowledge. It is possible to do, but it means that the humanities are actually much more challenging than many disciplines, because you have to understand the ways that those disciplines produce their knowledge, and the questions they ask, and then find ways to move beyond their limits.
The statement I just made, that disciplines have limits, is controversial, especially to people who have been trained in a particular discipline. My own training is in philosophy, but I am very aware of the limits of my own field and my own training. In particular, I am aware of the limitations of the kinds of questions I was allowed to ask. Philosophers ask about the nature of things, and try to clarify ideas as much as possible. They explore the very humanistic questions as well - what makes us human, what is the experience of being human like? But philosophy doesn't ask about its own history very much (for instance), or its own place of origin. That sounds strange - of course there's a lot of discussion about the history of philosophy. But I mean that philosophers assume that their objects of study are universal, that they didn't come from anywhere specific. So the discussion about the origin of ideas is usually about the ideas themselves, rather than the circumstances of their production.