quid n.1

"portion of food voluntarily forced into the mouth by the stomach of a ruminating animal," Old English cudu "cud," also "gum, resin, mastic," earlier cwudu, from Proto-Germanic *kweduz "resin" (source also of Old Norse kvaða "resin," Old High German quiti "glue," German Kitt "putty").

"a trifling nicety in argument, a quibble," 1530s, from Medieval Latin quidditas "the essence of things," in Scholastic philosophy, "that which distinguishes a thing from other things," literally "whatness," from Latin quid "what," neuter of indefinite pronoun quis "somebody, someone or other" (from PIE root *kwo-, stem of relative and interrogative pronouns).

The sense developed from scholastic disputes over the nature of things. Original classical meaning "real essence or nature of a thing, that which distinguishes a thing from other things and makes it what it is" is attested in English from late 14c. (quidite).

1610s, "a pun, a play on words," probably a diminutive of obsolete quib "evasion of a point at issue" (1540s), which is based on Latin quibus? "by what (things)?" Its extensive use in legal writing supposedly gave it the association with trivial argument: "a word of frequent occurrence in legal documents ... hence associated with the 'quirks and quillets' of the law." [OED].

Latin quibus is dative or ablative plural of quid "in what respect? to what extent?; how? why?," neuter of relative pronoun quis (from PIE root *kwo-, stem of relative and interrogative pronouns).