I am not sure your "I am going to prove you wrong" is the right approach with this player. He is not sticking to it to be awkward but because he finds the explanation satisfying. If I were you I would try and provide him with an alternate explanation of how magic and armour interact to replace the one he envisages.
As far as those who employ magic while also wearing armor you might look to the Norse/Nordic Myths. Many gods and users of magic (elves, dwarves, giants, etc.) use magic and also wear armor. It was cultural because warfare was a natural part of the society, and magic was not divorced from the ideals of the larger background. The same is often true of Celtic and Irish lore and myth. Look also to ancient Greek myth and the Bible, where users of magic an marvelous powers (not people we would think of as Wizards per se, but rather people we might think of as Sorcerers) were also often warriors.
I think Ydars' point is a very good one though. If an explanation is provided for the way magic works which is basically a corollary of our electromagnetic spectrum then it makes sense that conductive metals would disrupt or maybe even disperse magic. Magic would then be a form of energy related to electromagnetism and would be sensitive to the same types of conductive and non-conductive influences as electricity, for example. (Meaning rubber gear might have the same effect.)
However if magic were sensitive to certain materials in other ways (let us say iron concentrates magical force) then iron armor might encompass an advantage that leather did not possess, or even that bronze did not possess.
Then again one might be able to treat metallic armor with counter-materials which would negate or disperse the negative influence of any particular metal, or any metals.
Then again one can imagine magic being used to develop alloys and exotic materials (this is exactly how certain forms of magic are employed in my world setting by the Elves and Eladrin and Giants and others) with totally unique properties that allow for the production of almost weightless armor or compound armor types (similar to modern ceramics) which are much harder than metal, cheaper, have beneficial effects in regards to magic, or which are even disposable. For instance the Eladrins developed a form of armor which when soaked in certain chemicals hardens and shapes itself to the wearer. When sufficiently damaged or the wearer has no more use of it then it is doused in another set of chemicals where it loosens again and can be then disposed of. It is very effective against missile fire. The giants developed vests and other garb in which they can place alloyed pellets which are extremely effective against swords and knives, less so against missiles and spears, but the pellets are easily exchanged and the vest is disposable.
As far as I can see you have several possible solutions to the problem which might satisfy the player. Come up with a rationale which is not related to the "electromagnetic theory" of how magic operates. Develop a theory in which metals or whatever armor types you allow may actually positively influence the practice and use of magic. Develop counter-force materials with which he could line his armor that would negate disprove or disruptive effects (assuming there are any) of metal armor. Use magic or other means, such as technological advances in the construction of armor to develop armor types that are non-metallic but are jus as effective for defense, if not more so, for use by Wizards.
If you think about it, in any culture in which magic really functioned it would not be long at all until some Wizard decided that he would use his talents to develop experimental armor to give him the same, if not a better advantage, than that enjoyed by ordinary combatants.
If I were a Wizard one of the first things I would do is develop my own experimental substances, armors, and weaponry, both for my own benefit and in order to make a profit through sales to others. You would be looking to your own interests and you would have an easy and ready-made source of income generation.
If magic can be used to do things like Stop Time and Move Earth, you know it could be relatively easily employed in the development of new types of armor and other useful equipment and tools.
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