In the original Pokémon Red/Blue, when you encounter your rival in Lavender Town, he asks whether or not you know what it's like to have one of your Pokémon die. 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 Pokémon 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 all of this, your rival never outwardly tells you that you're responsible for the death of his Pokémon. 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. Although he tells himself that he doesn't hold you responsible, he subconsciously holds a great deal of resentment 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 than you…defeating you…and to eventually make it to the Pokémon League. Mere moments after he became Indigo League champion, he was defeated…by you. Although he fulfilled his promise to his fallen Pokémon, 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. During the course of the game, you steal your rival's innocence, crush his dreams, and ultimately snatch away the love of his own grandfather. Oh, and by the way, your rival doesn't have any parents. He's an orphan.