The above quotation is attributed to Winston Churchill, but to my mind it expresses Yanguan's point of view quite well.
Rhinoceros horn is known as black ivory, and was once used to fashion ornate objects for the emperor of China or for the very wealthy. A fan made of rhinoceros horn must have been a precious gift from a royal patron, an object of special significance.
What is Yanguan asking for, anyway -- either when he asks for the fan, or the rhinoceros? And what does the attendant mean when he says that the fan is broken?
The Chinese Zen tradition reveres the ability to discuss such matters without giving away any family secrets (i.e., without openly discussing the core of the matter). I don't think there's any danger of me doing any serious harm, so I'll say a few things about this.
What happens when you discover that the most precious of things is irrevocably, irretrievably, and irreparably broken? You might not recognize this as a promising condition, but Yanguan seems to be saying it is. So promising, in fact, that instead of sympathy, he offers a challenge. Note that this isn't perfectly aligned with the trite cliché that suggests we make lemonade when confronted with an abundance of lemons. There's a single nail left holding the board in place, and Yanguan is pulling it out.
It's almost giving away too much just to ask: what is the relationship between the fan and the rhinoceros?
One of my favorite teachers of all time is Yúnmén Wényǎn (雲門文偃), whose dharma name means Gate of the Clouds. There's a story about this curmudgeon that resonates with the rhinoceros.
A monk asked Yunmen, "What happens when the leaves have fallen and the tree is bare?"
Yunmen replied, "The body of the tree is revealed in the golden wind."