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Psychic only had one weakness - Bug. And the only bug-type damaging moves were Leech Life, which is weak as fuck, and TwinNeedle, exclusive to Beedrill, who sucks (And is part poison).
They should be weak to ghost, but due to programming error, they were actually IMMUNE to ghost. But even if they were weak to, the only ghost damaging move was Lick. Night Shade doesn't count cause have fixed damage.
Add to this the fact that the special stat was used to calculate both the attack and the defense when using special moves and that every psychic type had good special stats.