-아/어서 gives the reason or the preceding step, and 끼다 covers anything that goes around or into something: glasses, rings, a headband, a SIM card. 눈이 나빠서 끼는 거야 'do you wear them because your eyesight is bad?'; 유심을 직접 구매해서 끼고 'buy a SIM yourself and put it in'. It also stretches to squeezing in among people — 미국 리그 가서 껴서 하니까, joining an American league.