fault-finding (n.)

late 13c., faute, "deficiency," from Old French faute, earlier falte, "opening, gap; failure, flaw, blemish; lack, deficiency" (12c.), from Vulgar Latin *fallita "a shortcoming, falling," from Latin falsus "deceptive, feigned, spurious," past participle of fallere "deceive, disappoint" (see fail (v.)).

The -l- was restored 16c., probably in imitation of Latin, but the letter was silent until 18c. Sense of "physical defect" is from early 14c.; that of "moral culpability" (milder than sin or vice, but more serious than an error) is first recorded late 14c. Geological sense is from 1796. The use in tennis (c. 1600) is closer to the etymological sense.

Old English findan "come upon, meet with; discover; obtain by search or study" (class III strong verb; past tense fand, past participle funden), from Proto-Germanic *findan "to come upon, discover" (source also of Old Saxon findan, Old Frisian finda, Old Norse finna, Middle Dutch vinden, Old High German findan, German finden, Gothic finþan), originally "to come upon."

The Germanic word is from PIE root *pent- "to tread, go" (source also of Old High German fendeo "pedestrian;" Sanskrit panthah "path, way;" Avestan panta "way;" Greek pontos "open sea," patein "to tread, walk;" Latin pons (genitive pontis) "bridge;" Old Church Slavonic pǫti "path," pęta "heel;" Russian put' "path, way;" Armenian hun "ford," Old Prussian pintis "road"). The prehistoric sense development in Germanic would be from "to go" to "to find (out)," but Boutkan has serious doubts about this.

Germanic *-th- in English tends to become -d- after -n-. The change in the Germanic initial consonant is from Grimm's Law. To find out "to discover by scrutiny" is from 1550s (Middle English had a verb, outfinden, "to find out," c. 1300).