Because the question is supposed to "point directly at your mind" like the finger pointing at the moon. The answer could not do better. In fact, you learn more from trying to solve an apparent contradiction. If anything, you learn at least that you are frustrated over not getting it. What matters most is not the object (a koan, a hua tou) but how you hold it in mind, what it does to your mind, how you try to make sense of it, etc.
The funny thing is that we are so habituated to run after external objects and dive into them that it is difficult to look inward. A proof is that we are more concerned with the object (the koan) than we are with our mind. We forget to pay attention to what our experience tells us, not of the object we experience, but our mind that experiences. Because of this, we know little of the mind, including our own. It is easy to recognize a tree when we see one; it is way more difficult to recognize attachment, anger, belligerence, spite, etc. when they arise in our continuum because we seldom look inward, we are not familiarized with it.
As far I understand, the point with Hua tou and Koan is rather to stay with it and learn from how you relate to it. For instance, why is it that contradictions make you unsettled? How do you relate to frustration? Does frustration even arise when you try to solve a case? What makes you think it has to be solved? How do you try to make sense of things?
In Vipassana, some do what they call "meditation with an anchor" (the anchor often being the breath). Here, it is quiet similar. You learn a great deal by trying to stay with an object such as a Hua Tou. You learn why it is difficult to stay with it, why you lose it over and over again, etc. So it is not the answer that matter much.
Kazuaki Tanahashi 's introduction to Dogen's Shobogenzo is quiet informative and very enjoyable. But then, I am not that qualified when it comes to anything different from Tibetan Buddhism.