hair-splitting n.

Old English hær "hair, a hair," from Proto-Germanic *hēran (source also of Old Saxon, Old Norse, Old High German har, Old Frisian her, Dutch and German haar "hair"), perhaps from PIE *ghers- "to stand out, to bristle, rise to a point" (source also of Lithuanian šerys "bristle;" see horror).

Spelling influenced by Old Norse har and Old English haire "haircloth," from Old French haire, from Frankish *harja or some other Germanic source (see above). Hair-dye is from 1803. To let one's hair down "become familiar" is first recorded 1850. Homeopathic phrase hair of the dog (that bit you), remedy from the same thing that caused the malady, especially a drink on the morning after a debauch, 1540s in English, is in Pliny.

1580s (transitive and intransitive), not found in Middle English, probably from a Low German source such as Middle Dutch splitten, from Proto-Germanic *spleitanan (source also of Danish and Frisian splitte, Old Frisian splita, German spleißen "to split"), from PIE *(s)plei- "to split, splice" (see flint).

U.S. slang meaning "leave, depart" first recorded 1954. Of couples, "to separate, to divorce" from 1942. To split the difference is suggested from 1715; to split (one's) ticket in the U.S. political sense is attested from 1842. To split hairs "make too-nice distinctions" is from 1670s (split a hair; the figurative image itself is implied in Shakespeare). Splitting image "exact likeness" is from 1880. To split the atom is from 1909.