Fighting types were bad because Psychic types were good, and that's about it. Psychic is perhaps the most infamous example of an overpowered type in all of Pokemon -- in Gen 1, they were only weak to Bug, and Bug moves were terrible. Most were ridiculously strong, too -- Mewtwo, Alakazam, Slowbro, Exeggutor, and the rest were all very capable of putting up a strong fight. Every team essentially had to have a Psychic type because of how good they were, so as a result, Fighting types weren't used much.
Fighting types did have things going for them, like being able to hit Chansey, Snorlax, and Tauros with super effective STAB, but overall the risk just wasn't worth the reward when every serious competitive team had a Psychic type on it. They were better in-game, as not every opponent had something to hit them super effectively, but obviously still had to be careful around foes like Sabrina and Agatha.
