The name came from the way the American lines looked like on a situation map. Initially St Vith was defended with a horseshoe type defense. After several days of fighting the Americans were pushed out of St. Vith but still held the same basic type of defense. The Germans were able to push in the open ends of the horseshoe somewhat. it wans't until Dec 23rd that the Americans began to pull out of the "Goose Egg"
The problem with a "Goose Egg" or a "Bulge" is that if the other side can amass enough forces they can cut off your "Egg" or "Bulge" at the the base and then the forces in the "egg" are cut off and quite probably wiped out.
The strategy for packing the shoulders of a penetration and attacking at the base goes back to WW-I.
Regards
alfa6 ;>}
Thanks!