Actually, our word “vermin” comes from the German word for worms, which would be a maggot or caterpillar.
The English word “vermin” comes from the Latin word “vermis”, meaning animal pest or worm, through the French word “vermine”. The English word “worm” and the German word “Wurm” mean the same thing and they share a common proto-Germanic root. Latin vermis and English worm derive from a common Indo-European root.
http://www.myetymology.com/english/worm.html
http://www.myetymology.com/english/vermin.html