Fighting is super effective againts dark for the reason that fighting types represet honorable way to fight while dark types represent the dirty way to fight, and honorable>dirty. As for bug being super effective against dark and psychic... idk.. maybe they have... bug allergies?
Best guesses: FIghting>Dark since Dark types are dishonorable in their methods while fighting types fight with honor. Bugs>Psychic Bugs are a common phobia and considering that psychic is associated with the mind... Bugs>Dark Um... Bugs thrive in the dark?
Fighting>Dark: Three words- Cheaters Never Prosper.
Fire>Steel: Chinese Elements, Fire melts Metal Grass>Ground: Chinese Elements, Wood breaks Earth by growing in it. Ice>Dragon: Cold blooded things hate the cold Bug>Dark: It's hard to sneak up on a swarm of bugs.
Oh, and this: http://tvtropes.org/pmwiki/pmwiki.php/WMG/PokemonTypeMatchups