면서 지나가다

pass by while doing X

지나가다 is passing by, and the while form attaches what was going on at the time: a parade going past with a roar, a comet passing while scattering dust it held in ice, someone going by mid-workout, cars going past honking. It also covers letting a moment pass, as in the lines where someone thought it might be an anniversary or somebody's birthday and just let it go by. Several lines pair it with the verb for saying, describing remarks that were tossed out in passing.