Was the fight that broke out between the brother and his sister, due to spraying perfume, and which escalated into a brawl after she called him "you animal," predestined and written by Allah?

Nothing happens in the universe except by divine decree and preordainment, as Allah the Almighty says: "Indeed, We created all things in due measure" and "Say: 'Nothing will befall us except what Allah has decreed for us.'" Belief in divine preordainment (Al-Qadar (definition)) is one of the six pillars of faith, and a servant's faith is not complete without it. In the Hadith (definition): "A person does not believe until he believes in Al-Qadar, its good and its evil." And in another: "Even if you spent Mount Uhud's weight in gold in the way of Allah, Allah would not accept it from you until you believe in Al-Qadar, and know that what befell you could not have missed you, and what missed you could not have befallen you. And if you were to die upon other than that, you would enter the Hellfire." As for the interpretation of what happened, it is not unlikely that the sister considered her brother to have wronged her, so she became angry, and then he became angry when she addressed him in a manner he deemed inappropriate.