Kids fight when they can get away with it. In some households one child is clearly the favorite or is perceived as the favorite by the children. In a situation like this, the favored child may instigate a fight simply because he can. Children can be corrupted by power as easily as adults. Be certain the real problem doesn't lie with perceived favoritism on your part.
Kids fight when one child feels slighted by the other.
Often older siblings reach a stage when playing with the younger child becomes socially unacceptable. Especially do not force public play - this can lead to embarrassment and greater sibling resentment. Kids fight out of habit. Sometimes bullying and spitefulness become habits between siblings. Erase points for any meanness or belittling.