Answer:
Once, Bali chased a demon Mayavi after killing his brother Dundabhi. Mayavi entered into a cave where Bali followed him. Bali too followed him into the cave. But before entering he cave, he instructed Sugriva to wait outside for a fortnight. He also said that if he did not come out of the cave after fifteen days, Sugriva would understand that Bali had been killed. After a month, He saw blood coming out of the cave and assumed that Bali was dead. Sugriva returned to the kingdom as a king. But Bali was alive. When he came back and saw Sugriva running the kingdom of Pampapuri,he became furious. He drove Sugriva out and enslaved his wife as well. Sugriva was hiding in Rishiyamooka mountain, because of curse of Sage Matang, this place was safe.
This is the crux of what and why it happened, the incident that made brothers enemies. Y