Damaging rhymes with:
imaging, rummaging, acknowledging, averaging, disparaging, encouraging, foraging, hemorrhaging, imaging, leveraging, messaging, micromanaging, mismanaging, mortgaging, packaging, pillaging, presaging, ravaging, repackaging, rummaging, salvaging, savaging
Damaging sounds like:
dancing, dehumanizing, demagoguing, demjanjuk, demjanjuk's, demonizing, denison's, denizens, denkins, denouncing, dimensions, diminishing, dinkins, dinkins', dominicans, doomsaying, downsizing, downsizings, downswing, duensing, dungeons