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.