Vali was invincible. He was already strong and when he fought someone, he took half their strength. Vali would fight anyone. He could fight anyone.
Not long ago, Vali chased a demon into a cave. He was gone for quite a while, terrible noises came from the cave, and it was feared he had finally been overcome. Fearing the worst, Vali's brother Sugriva had the cave closed up. For surely, if something in that cave could kill the mighty Vali, the entire kingdom, maybe the world, would be in danger if it came back out!
Fortunately for the world, and ultimately unfortunately for Sugriva, Vali lived! But now Vali was sure that his brother was trying to get rid of him and wanted to take everything that was his. Because Vali would not listen to reason or explanation, the brothers fought. Fearing for his life, Sugriva fled to a place Vali could not follow. The fight continued, but Sugriva was not in danger of losing his life over a misunderstanding.
Vali took Sugriva's wife and continued to be immune to any pleas. For all his strength and prowess in combat, Vali's ears were closed to reason. Vali knew best, and nothing would change that.
Sugriva lived without his wife and without his people for a time. When he met the hero Rama, he talked through the situation with Vali and asked for help. Rama agreed to help Sugriva defeat his brother who would not listen to reason.
On the day Sugriva came to challenge Vali, with Rama in tow as his secret weapon, Vali was again immune to reason. Vali's wife Tara pleaded with him not to take the fight. She knew in her bones that nothing good could come of the situation. Again, Vali did not listen to anyone else - Vali knows best, Vali is invincible.
One arrow was all it took for the hero Rama to put an end to Vali. Before he died, Vali's ears were finally opened to reason.
An illustration from a 17th-century copy of the Ramayana in the collection of the British Library: "Outside the palace of Kiskindha, Sugriva roars out his challenge to his usurping brother Bali, so that the very birds fall out of the sky in fright, while Rama and Laksmana and the other monkeys look on from the right. On the left is the monkey king's palace, from which Bali, his queen Tara and ministers have emerged on hearing the uproar. Tara advises him not to fight, but to no avail. Bali and his party all wear human costume, except for turbans, while Bali himself wears a crown."
Source: Wikimedia and ultimately the British Mueseum
Based on: The Ramayana: A Shortened Modern Prose Version of the Indian Epic by Kamban / R. K. Narayan, 1972 (Kindle edition)
Author's Note: This ended up being a very simplistic retelling/overview of Vali and his closed ears. I may revisit this at some point because it isn't quite what I wanted to do, but it's where I ended up!