Why is the cross-bill so called?

Because the mandibles of the beak do not lie upon each other, with their lateral edges in opposition, as in other birds, but cross, or curve to the right and left, and always in opposite directions to each other. In some specimens, the upper mandibles curve downwards and to the left, the under portion turned upwards, and to the right. - Mr. Yarrel, in the Zoological Journal.

Why is the cross-bill so destructive in orchards?

Because it feeds upon the seeds of the apple, by cutting the fruit asunder with its well-constructed mandibles, in order to obtain the kernels.