Someone who is hostile to you and who you really do not like is an example of someone who would be described as your enemy.
A person who opposes all legislation protecting animals is an example of someone who might be described as an enemy of animal rights.
A country who has declared war on the U.S. is an example of an enemy of the U.S.
Origin of enemy
- Middle English enemi from Old French from Latin inimīcus in- not in–1 amīcus friend
From American Heritage Dictionary of the English Language, 5th Edition