The decoration on this cup, pairs of various kinds of birds including the phoenixes and the cranes, would imply wishes for longevity and a harmonious marriage.
Two rhinoceros horn cups in the Chester Beatty Library include the two types of birds seen on this cup. See J. Chapman, The Art of Rhinoceros Horn Carving in China, London, 1999, p. 187, no. 253, for a detail of a cup with a pair of cranes and no. 254 for a cup with a pair of phoenixes. The style of carving on both of these appears to be very similar to that on the present cup.