Chickens do fight each other for several reasons which include;
1.Food; they tend to fight when under starvation and no adequate food supply.
2. Space/territory; They also fight when there is no adequate space i.e congested in a confined area, also to prevent any stranger from intruding their territory (most especially the cocks/roosters).
3. Courtship; when there is more than one cock/rooster in a flock hens, the cocks/rooster tend to fight each other/one another in order to compete for a hen for mating, the victorious one would be the one to mate with the hen.
4. Protection; A hen becomes very aggressive and will fight other chickens to protect her chicks when she feels threatened.
There might be other reasons though, but these are some of them.