She gets pissed when the Empress warps the point of the story to be comedic because it feels like she's dismissing her feelings or concerns.
Pretty sure the bigger reason for the upset is that the second story recontextualizes the first story. The first story is a story of love and desire, the fish wishes to be a part of the bird's world and, if only the bird knew, perhaps it could be.
But the second story gives the bird's perspective to reframe it into a story of predation. The bird is hunting the fish and, if the fish were ever to meet the bird, the bird would simply kill the fish.
A more subtle thing happening is that she seems to be presenting the emperor as the bird in the second story where the emperor felt like the fish in the first story, which is another act of reframing. This recontextualizes the emperor's desires and love and predatory, of an attempt to invade the space of those "he" desires and to hurt them. It makes the emperor out as a sort of villain for even having these desires in the first place.