[angry dispute] mid-14c., querele, "dispute, altercation," also "ground for complaint," from Old French querele "matter, concern, business; dispute, controversy" (Modern French querelle) and directly from Latin querella "complaint, accusation; lamentation," from queri "to complain, lament," from Proto-Italic *kwese-, of uncertain etymology, perhaps, via the notion of "to sigh," from a PIE root *kues- "to hiss" (source also of Sanskrit svasiti "to hiss, snort"), which is not very compelling, but no better etymology has been offered.
In Middle English also of armed combat. Old English had sacan. Sense of "angry contention between persons" is from 1570s.
A quarrel is a matter of ill feeling and hard words in view of supposed wrong : it stops just short of blows; any use beyond this is now figurative. [Century Dictionary, 1897]
"short, heavy, square-headed, four-edged bolt or arrow for a crossbow," mid-13c., from Old French quarel, carrel "bolt, arrow," from Vulgar Latin *quadrellus, diminutive of Late Latin quadrus (adj.) "square," related to quattuor "four" (from PIE root *kwetwer- "four"). Now-archaic sense of "square or diamond-shaped plane of glass" is recorded from mid-15c., from Medieval Latin quadrellus "a square tile."
late 14c., querelen, "to raise an objection, dispute; rebel;" 1520s as "to contend violently, dispute angrily, fall out," from quarrel (n.1) and in part from Old French quereler (Modern French quereller). Related: Quarrelled; quarrelling.