the.com/insinuation

means A hint or implication of something (usually unflattering) dropped into conversation without ever being stated outright, leaving the speaker deniability and the listener to connect the dots.

from From Latin insinuare, 'to work into, to wind one's way in' — built from in- ('into') plus sinuare, 'to curve or bend,' the root behind 'sinuous.' The original image is physical: something snaking its way in through a curve or fold, like a hand slipping into a sleeve or a current finding a bend in a riverbank. By the time it entered English, that winding motion had turned figurative — an insinuation doesn't walk straight through the door and announce itself, it curves in sideways, edging into the mind without ever being formally let in.