I always thought that Psychic types held a defensive advantage over Fighting-types for the same reason the Byakugan and Sharingan gave advantage over physical moves in the Naruto world (I kinda dislike using this an example but meh~). Instead of actual visual prowess, Psychic types can probably foresee where a Fighting move may land and adjust accordingly to lower the impact. Inversely, Dark (Evil type in japanese IIRC) types and Ghost types probably invade a Psychic types mind and use their power of foresight against them or cloud their judgment, which is why they would be super effective against Psychic types.
Also, being a Psychic type doesn't necessarily mean the Pokemon is intelligent. (e.g. Slowbro)