1620s, "to fall, drop, or stomp (on something soft) with crushing force," possibly imitative of sound made in the process. The figurative sense of "suppress completely" is first recorded 1864. Related: Squelched; squelching.
Middle English quenchen, "to extinguish, put out" (heat, light, fire, also of desire, hunger, thirst), also figurative, "to bring to naught, eliminate, render ineffectual" (c. 1200), Old English acwencan "to quench" (of fire, light), from Proto-Germanic *kwenkjanan, probably a causative form from the source of Old English cwincan "to go out, be extinguished," Old Frisian kwinka. No certain cognates outside Germanic; perhaps a substratum word. Especially "to cool or extinguish by means of cold water," hence "to drench in water" (late 15c.). Related: Quenched; quenching.
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Harper, D. (n.d.). Etymology of quelch. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/quelch