Why are ㄲ ㄸ ㅃ compared to sky, stop and spy? They look nothing alike.

Listen to the k in sky and the k in kite — they are not the same sound. After "s", English drops the puff of air, and that airless k is almost exactly Korean ㄲ. The comparison is about the puff, not the spelling. Add the tight, held-back feeling in your throat and you have it.