I know this was an old question, but it still really intrigued me, so here are my thoughts on each one.
My chart is as follows:
Type of pokemon: weaknesses
Fighting types are trained at combat, while a normal type is not. It's like Jackie Chan fighting a Random guy on the street. Chan would have the advantage
due to his training.
Fire: water, ground, rock
Water puts out fire, soil and rock can be used to put it out as well.
water: electric, grass
plants absorb water and water is a very good conductor of electricity.
Earth is not a good conductor of electricity.
grass: bug, poison, flying, fire, ice
Fire and ice are super effective because most plants cannot survive in extreme temperatures. Fire burns up the plants while the cold can freeze and kill
them. Bugs and flying types are strong because many insects and birds eat plants. Poison is a common killer of plants too. (despite many of them being
poisonous themselves, explaining the common grass/poison type combo.)
Fighting: Psychic, Flying
Psychics are strong against them completing the brains over brawn theme, and things in the sky have the advantage over things stuck on the ground. Like the comic pokemaster posted, "have you ever tried to punch a bird?"
Ice: fire, rock, steel, fighting
Fire melts ice. Stone is harder than ice and can break through it, as is the case with steel (a mechanical device is capable of drilling through stone.
Martial artists can demonstrate their strength by breaking through things like wood, stone, and in this case, ice.
Poison: psychic, ground
The earth absorbs toxins and is able to heal itself in time. Psychic types can have the "mind over matter" theme as well as use their psychic powers to keep the toxins at bay.
ground:water, grass, ice
Water erodes soil, plants grow and get nutrients from the earth, and ice can crack through things it freezes. It could also be something like continental drift.
Flying:electric, ice, rock
Lightning is drawn to metal, as well as tall objects;while not necessarily tall, flying types usually take to the sky, making them more prone to electric moves.
Ice is bad for birds since many of them go farther south for the winter. The piercing cold makes it harder for them to fly. Rocks weigh down birds and can be
projected at them for damage. It might also be based on the saying "killing two birds with one stone."
Psychic: bug, dark, ghost
This one was my personal favorite to come up with. Psychic types are usually pokemon that depend their mind and thoughts very much. Fear is all in your mind, and three of the most common fears for a human are insects, the dark, and death. These fears manifest themselves as weaknesses. Dark was also put in to balance out psychic types, who were very overpowered in generation I. Bugs can also break your concentration, which psychic types rely heavily on.
Bug: fire, flying, rock
Fire and rock are pretty self explanatory. You can crush a bug or burn it. Flying types are the birds that eat insects.
Rock: Water, grass, fighting, ground, steel
Water breaks rock down very slowly and makes it into sediment; Plants can grow their way through rocks; Martial artists break through rocks as training;
the ground can contain and swallow rocks with earthquakes, and metal is stronger than stone. Think of a drill.
Ghost: Ghost, dark
Ghosts aren't solid, so it takes a ghost to beat one. Anything else would just go through it. Ghosts are typically thought of during night time.In fiction, They wouldn't normally appear during the daytime, so the best time to strike them, when they are "seen," is at night, when there is darkness.
Dragon: dragon, ice
Dragons are mythical creatures, and they're believed to be so powerful, that the only thing that can defeat them is another dragon. Dragons resemble reptiles
a lot, so they are likely cold blooded. Low temperature would affect them very badly if that were the case. Though that would mean they would also be weak to fire.
Ice was probably thrown in to make sure they didn't become too broken. (since there weren't any reliable dragon moves in gen I, battling lance would be a pain.)
Ice helped as a fairly easy to obtain type and balance things out.
Dark: bug, fighting
Fighting is super effective since they typically fight with honor, as opposed to the dark types more sneaky tactics. This is the light conquering dark theme
once again. Many insects have very poor sight, so having darkness won't be much of an advantage. Since dark types use that as something of a stealthy advantage,
and bugs are used to fighting such opponents, it gives them an edge. It was also to help bug types a bit more since they didn't have a ton of types to be
super effective against.
steel:fire, fighting, ground
Intense heat melts metal. Steel was made from the earth, so the earth is connected to it. To kill the earth-the source of steel-would be harming steel itself. However, the earth can survive without steel is it had before steel existed. Nature beats machinery I guess. Fighting types being super effective seems to follow the "man over machine" theme. It was also to help give it something of an advantage so it would see more use. After the psychic regime of Kanto, it was a necessary one. (though I honestly thought poison types could use a bit of help too. Poison can pollute waters, acid can eat through metal, there's tons of stuff they had to work with, but it's strong against just one measly type.)