give the slip

early 14c., "to escape, to move softly and quickly," from an unrecorded Old English word or cognate Middle Low German slippen "to glide, slide," from Proto-Germanic *slipan (cf. Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"), from PIE *sleib-, from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)).

From mid-14c. with senses "lose one's footing," "slide out of place," "fall into error or fault." Sense of "pass unguarded or untaken" is from mid-15c. That of "slide, glide" is from 1520s. Transitive sense from 1510s; meaning "insert surreptitiously" is from 1680s. Related: Slipped; slipping. To slip up "make a mistake" is from 1855; to slip through the net "evade detection" is from 1902.