rara avis (n.)

[thin, few, unusual] late 14c., "thin, airy, porous" (opposed to dense); mid-15c., "few in number and widely separated, sparsely distributed, seldom found, very infrequent;" from Old French rer, rere "sparse" (14c.) and directly from Latin rarus "thinly sown, having a loose texture; not thick; having intervals between, full of empty spaces" (antonym of densus). Sometimes reconstructed to be from a PIE root *ere- "to separate; adjoin."

"Having the particles not close together," hence "few in number," hence, "unusual." Sense of "remarkable from uncommonness," especially "uncommonly good" is from late 15c. (Caxton). Related: Rareness. In chemistry, rare earth is from 1818.

Rare implies that only few of the kind exist : as, perfect diamonds are rare. Scarce properly implies a previous or usual condition of greater abundance. Rare means that there are much fewer of a kind to be found than may be found where scarce would apply. [Century Dictionary, 1895]

"large cage or building where birds are reared or kept," 1570s, from Latin aviarium "place in which birds are kept," neuter of aviarius "of birds," from avis "bird" (from PIE root *awi- "bird").