Earthly Branch (Animal) Relationship
The attraction relationship of Earthly Branches is from the relative positions (in the sky) of the Sun and the Moon in an old calendar system. Also, all animals in the Chinese Calendar have a sequence number. If the total of two sequence numbers is 15 or 3, then they have the attraction relationship.
Enmity Relationship (Fighting)
Just like the Stem relationship, the enmity relationship is from the relative positions of the elements. The Chinese consider a "face to face" conflict as the enmity relationship. Wood is in the east and faces Metal in the West. Water is in the north and faces Fire in the south. They are unlike each other, so they live in different places. Also, same genders reject each other.
There is an Enmity relationship when the difference between the animal's sequence numbers is six.