Why can't Magic-Users wear armor? Because they can't that's why. I have read articles, most recently in the new issue of Footprints, that postulate that M-Us can't wear armor because of the restrictiveness of movement while in armor. This is often accompanied by the rationalization that you need to be trained to wear armor. D&D players ALWAYS get this wrong. I have been a heavy armored fighter in the SCA* for a long time and I can tell you that I have had clothing more restrictive than my armor. Armor is designed so that you can fight in it. It is not complex to get in and out of. I have never liked the idea that, say, Platemail makes you slow. It doesn't. It's not hard to move in. I have seen a guy do cartwheels wearing full plate. Plate is articulated to bend where the human body bends and it's weight is so well distributed across the body you barely feel it.
Learning to fight isn't easy, not being good at it anyway. Wearing armor is. I get the rationalization that M-Us can't use various weapons. I think they should suck more with the weapons they do get honestly, because learning to be good with a weapon takes time and time is what M-Us use to learn magic. I can understand the restrictions against shields. In a realistic game I wouldn't ban anyone from picking a shield up, but honestly, until you learn to use it, your shield is not your friend. Properly trained in the use of a shield it can become the keystone of your defense. I have not thought the shield was given it's due in any RPG I have ever played (or read, or heard about) but that's not the point here**.
Magic-Users should be weak fighters, they spend all their time in bookish pursuits. That they get any weapon skills at all is pretty unrealistic, it's like saying every M-U's hobby is a martial art, that's where they picked up the skill with the dagger (or staff or dart or whatever), they spent all their free time learning that. That's like saying every computer nerd has as his primary (or sole) hobby Kung-Fu. Simply unrealistic, but we allow it for the sake of the game. The armor restriction, whether it was placed for the sake of balance or just to differentiate the classes needs to be accepted for the same reason. Realistically, strapping on armor is simpler than learning the basics of fighting with a quarter staff, particularly since M-Us are pretty bright guys and they'd only need to be shown how to do it once, or if no one was around to show them they'd probably be able to figure it out on their own pretty quick. They are all geniuses after all.
Now somebody will be thinking that maybe it should just be because magic and iron can't be used together (actually that's a theme in Robin Hobb's Soldier Son trilogy, which I recently read), then it'll be rebutted with the fact that M-U's use iron daggers and iron tipped darts and, sometimes, iron shod staves. Then the argument will come forth that that's a small amount of iron and therefore no big deal to the magic. Then the proximity of the rest of the iron encased party members will be called into the debate, followed by the reasoning that they aren't actually touching the chainmail clad fighter while casting spells. This will be followed by someone suggesting that if this is the case then M-Us should be able to wear leather or bronze armor (and use shields), so it must be based on the freedom of movement necessary to cast spells being restricted by the armor, which isn't true. If anything I would think the voluminous robes and cloaks and large floppy hats would be restrictive to movement.
Accept that somebody, probably Gary Gygax, made it a rule for gamist reasons, not realistic ones. It probably had something to do with trying to enforce the wizard archetype, wanting the M-U to look and act more like Merlin or Gandalf than Lancelot or Conan. There are a lot of gamist decisions in D&D dating back to Chainmail; Gary was a history buff and a sword and sorcery genre fan, he got lots of little things wrong but we still revere his memory because he invented the hobby we love.
* I know, everyone hates an “expert”, they ruin the gamey goodness by bringing in their expert opinions on what-ever topic. I am worse then most that way as a D&D player when you get me going, because I am a trained medievalist, living historian and SCAdian.
** I could rant about shields for a long time. My favorite style of fighting is sword and shield and I believe that the shield, when properly employed, is probably the single most important part of your defense. Much more important than body armor; right up there with the helmet, which also gets no love from D&D. SCAdians get some wrong impressions about combat too, since our safety rules have made our shields invincible and ruled out certain less honorable, less chivalrous actions, but I stand by my love of shields and now have a new D&D house rule that takes their importance into effect. Hackmaster basic actually has the best shield rules going that I have read in an RPG, but I have a few issues with the gamism in combat there too.