Latching rhymes with:
attaching, catching, dispatching, hatching, matching, patching, scratching, snatching, approaching, arching, attaching, beaching, belching, beseeching, birdwatching, bleaching, blotching, branching, breaching, breeching, broaching, bunching, catching, clinching, clutching, coaching, couching, crouching, crunching, dispatching, ditching, drenching, encroaching, enriching, entrenching, etching, fetching, flinching, hatching, hitching, impeaching, inching, itching, kitching, launching, leaching, lunching, lurching, lynching, marching, matching, melching, mulching, munching, outpouching, overarching, overreaching, patching, pinching, pitching, poaching, preaching, punching, quenching, ranching, reaching, researching, retouching, retrenching, rewatching, scorching, scratching, screeching, searching, sketching, slouching, snatching, snitching, squelching, stanching, stitching, stretching, swatching, switching, teaching, torching, touching, twitching, unflinching, vouching, watching, witching, wrenching