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We have 4 contenders for the worst type. Let's analyze them. (Bug isn't bad.)
>Rock
>Grass
>Ice
>Psychic
Let's go in order.
Rock is ironically a terrible typing defensively. Although lots of the Pokèmon in its pool are perceived as bulky powerhouses, rock is weak to the most undeniably common types such as steel, fighting, ground, water & grass. Besides that, it has almost no special defense. As for it's moves, it gets decent coverage with it destroying ice, fire, flying and bug. The only common types it can defend itself against fairly well is flying and fire, even then not making it that good.
As for grass, it's defenses are pretty shaky considering its pokemon get decent stats, but the types it's weak against make it a cancerous type to play with. Weakness to fire, flying, bug, poison and ice. Not only are 2 of those common, but all of those types' move distribution is wild enough to bring down all grass types. Offensively, it can fuck up water, ground, and rock. That's it. Three fairly common types, but the payout is not as good as the work done to it in battle.
As we all know, offensively, Ice is amazing. Every pokemon and their mother gets ice beam and blizzard and that shit fucks up not only grass, flying and ground, but fucking DRAGONS. Everyone wants this move no matter what for the coverage. However, defensively is where this typing falls flat. Weak to super common types such as fire, rock, steel, and fucking fighting. Now that's what I call a shitty defensive typing. Not only that, but only like 5 or 6 different ice types are actually viable in the current meta, the rest being slow and frail ice types only exisitng for their gimmicks.
Finally, we have Psychic. It is apparent that psychic is nothing special. Fucks up fighting and poison fairly well, but that's about it. As for it's weaknesses, dark, ghost and bug, simply put, you cannot send in your psychic type anymore. Super powerful pokemon in its pool, and super weak ones.