In a fantasy world full of magic, i want the elemental forms of magic to be strong against one another in a symmetrical way (meaning every element has the same amount of weaknesses and strengths). I do not specify how many strengths and weaknesses they should have, even though i would be happy to let each one be strong and weak against two others respectively. The elements are (fire), (earth / rock), (water), (air), (ice) and (metal / ore). Feel free to rearrange and reconnect them in any way that fits.
I am currently rebuilding an elemental magic system in a game i am playing, but i am having problems justifying some of the elements being strong or weak against some others.
First, the setting: If anybody knows it, i am building custom rules for The Dark Eye, a tabletop-rpg game that comes with its own setting. It is high fantasy, there are elves, dwarves and much of the other stuff you would expect from a tolkien-like setting. If thats any help, the backstory of magic becoming part of this world is a certain goddess breaking the rules and also a hole into one of the borders of dimensions and letting the power of magic flow into the mortal plane. It manifests in many ways, but the wizards guild is teaching the way of controlling it by weaving the flow of magic through willpower, gestures and incantations. Elemental magic is just one kind of many, but it is the one i am most interested in in this question. It allows the wizards to summon the element in form of attacks or elementals.
Because i do not want to rework all of the games rules i am bound to the choice of elements that exist in this world. I already tried my best thinking up how they relate to each other, but there are some connections that i am having trouble with. I drew up a chart of the elements and how i think they could relate to each other:
The direction of the arrows means "is strong against", e.g. "Water magic is strong against fire magic" (for obvious reasons). Giving each element two others which it is strong against resulted in a nicely mystic hexagon shape, but there are a few connections i am not sure about:
Fire -> Air - I maybe thought about air providing more fuel for the fire, thus increasing its strength while trying to attack or defend against it, but that sounds a little bit like an excuse. It's ok compared to the others, though.
Air -> Earth - Now, air could dry out earth to turn it into dust and blow it away, but rock also belongs to the earth element and really makes me unsure about this connection.
Earth -> Metal - This is one of the real bad candidates. I have no idea how to explain this, apart from metal not being too good at destroying earth and stone in a medieval world. This is true the other way around too, though.
Metal -> Air - This, too, gives me a real headache. I mean, metal is kind of immune to wind, but it is not particularly strong against it, either. Maybe attacks and elementals made from wind get disturbed by the solid structures metal forms? But then, earth would need to be strong against air, too.
Ice -> Earth - Frozen earth is more fragile? This one is not as bad, too, i guess, but could be a lot better.
Air -> Water - Honestly, i can not think of anything better than air "cutting more sharply" than water. I am very much not happy about this one either.
I kept rearranging and reconnecting these elements, but i just could not find a constellation that was satisfying. I am looking for someone to help me fix this constellation or provide an explanation that removes my doubts about my solution.