You rarely see a Korean woman without a fantastic pair of shoes- shined, formal and... suggestive of clean feet?
Feet are considered dirty in Korea- the dirtiest part of the body, in fact. Resting your feet on the couch, or close to someones head, is incredibly rude.
So, like the cleaning of the ears, massaging a loved one's feet is a selfless act. Children may be asked to massage their Mother, Father or Grandparents' feet. If a Korean girlfriend digs her thumbs into her man's soles, that's some serious loving.
One time I had Min over, and was stomping around in high heel boots. He suggested I take them off. Apparently it seemed as strange as the time I offered Chung a small tumbler of Soju from a bottle I picked up at the grocery store, seduced by the price alone: $1. Soju is to be consumed with a meal only- and shoes are to be removed at the door. Silly Canadian girl.
Nearly all Korean apartments have heated floors, so it makes sense to enjoy the warmth. Also, traditional restaurants, where you sit cross-legged on a pillow, provide a mat or a shelf on which to leave your footwear.
My question is this: If feet are so dirty, why remove shoes in the home? My guess is that Koreans see feet as dirty, but shoes as contaminated. You want your guests to feel at home, so you put up with the atrocities attached to their ankles.