How did 'quibus?' shift to mean 'evasion of a point at issue'?
_Quibble _probably originated as a rather ponderous learned joke-word. It is derived from an earlier and now obsolete _quib _‘pun’, which appears to have been based on quibus, the dative and ablative plural of Latin quī ‘who, what’. The notion is that since quibus made frequent appearances in legal documents written in Latin, it became associated with pettifogging points of law.
Word Origins (2005 2e) by John Ayto, p 408 Left column.
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).
The Word Detective also doesn't expound the semantic shift. I quote W. Rothwell's A Mere Quibble? Multilingualism and English Etymology published online on 9 Jan 2007, p 181.
The historical dictionaries of English show that 'quibble' poses a problem for the etymologists. The OED^17 offers no firm etymology for it, its first attestation in its modern sense of 'an equivocation, evasion of the point' coming from 1670, almost three and a half centuries later than the kevel of the Year Book. An earlier, now obsolete, sense of 'a play on words, a pun' is attested for 1611, with the verb 'to quibble' recorded for 1629, which might indicate that an earlier date for the noun could eventually come to light, since it is common practice for verbs to be derived from existing nouns. The dictionary suggests that 'quibble' may be a diminutive of the obsolete noun 'quib', attested 'a[nte] 1550', which it derives from the Latin quibus '"who, which", as a word of frequent occurrence in legal documents and hence associated with the quirks and quillets "of the law"'. However, the special relationship claimed between quibus and the 'quirks and quillets of the law' is not explained, and the proposed etymology will not stand serious scrutiny. The Latin quibus is a common term widely used outside legal documents, an everyday word belonging to the general register of the lexis without any particular concentration in legal works.