In the original Pokemon Red/Blue, when you encounter your rival in Lavender Town he asks why you’re even in Pokemon Tower if none of your Pokemon were dead. At this point in the game, he no longer has his Raticate that he used in previous battles. Your rival battle before this took place aboard the S.S. Anne. Your rival's Raticate sustained serious injuries from the battle... But, because of crowding and confusion on the luxury liner, he was unable to make it to a Pokemon center in time and the Raticate passed away.
The real reason your rival is in Lavender Town to begin with is to lay his deceased friend to rest. Despite this, your rival never outwardly tells you that you're largely responsible for the death of his Pokemon. He hides his grief and instead channels that energy into the motivation he needed to continue his quest to become Indigo League Champion. The death of his Raticate effectively destroys your rival's impish, childhood innocence.
He channels his anger towards you which further fuels his ambitions. Tearfully swearing upon his Raticate's grave to not fail in what he set out to do, he trains hard in hopes of becoming better that you... Defeating you... And eventually make it to the Pokemon League. Mere moments after he became Indigo League champion, he was defeated... By you. Although he fulfilled his promise to his fallen Pokemon, it was only for a painfully brief instant. In the end, your rival is scolded by his grandfather while you receive the professor's praise.