Why is Enkidu so strongly opposed to Gilgamesh's exercise of ius primae noctus?
It is not entirely clear from the text why Enkidu becomes enraged that Gilgamesh oppresses his people by taking the ius primae noctus -- that is, the right of the first night with each new bride before she goes to her husband. Some assumptions can be made by looking at what happened to Enkidu directly before he fought with Gilgamesh in the street. He has experienced a period of sexual excess, and a loss of his friends the animals with whom he formerly had run like a brother. He has lost his wild hair and has learned to dress and eat like the people in Uruk. Perhaps his own loss makes him sensitive to others' losses.
One day a man who was going to Uruk
Stopped to eat at the shepherd's house.
He told them he was hurrying to the marketplace
To choose for himself a virgin bride
Whom Gilgamesh by his birthright
Would sleep with before him.
Enkidu's face was pale
He felt a weakness in is body
At the mention of their king.
He asked the prostitute
Why this should be his birthright
She answered: He is king. (21)
Though it isn't stated, it appears that Enkidu has some sort of internal morality that is outraged by this injustice. He, in his simplicity, is the "noble savage" who has a stronger sense of morality than the urbane king. It is with this simplicity that Enkidu helps Gilgamesh become more human.
Text Source: Gilgamesh. Trans. by Herbert Mason. New York: Mentor Books, 1970.