There are many rules in the 1st edition AD&D books that contradict themselves, or make no sense. This is one of the main reasons why the initiative section and other parts of combat are such a mess. It seems that the rules were written over such a long period of time that impressions of how those rules should work changed during the writing. None of these contradictions are more glaring than when it comes to magical armor and how much or how little it affects movement rate and/or spellcasting.
In order to understand some of the problems with this rule, one has to first appreciate how Encumbrance was explained to the players. On page 101 of the PLAYERS HANDBOOK, we have a short section on encumbrance and what it means for the player character overloaded with armor, weapons, and adventuring gear. However, nowhere in this section does it differentiate between man-sized characters (humans, elves, half-elves, and half-orcs) and smaller-than-man-sized characters (dwarves, gnomes, and halflings). It is assumed by reading this section that all characters move at the same base movement rate of 12" and can carry the same amount of equipment (which, of course, is patently absurd). Imagine a 3' tall gnome carrying around the same weight of gear as a 6' tall human and being able to move at full speed! Now, remember, that 12" is a scale movement -- it does not mean that the character only moves 12 inches in a turn, but rather moves 120 feet (as 1 "scale inch" = 10 feet on the map). This means a character only moves at 120 feet in 10 minutes of exploration, or 120 feet in one round of combat. This is pathetically slow and has been criticized over the years as being "unrealistic." Compare it with the movement rate of 3rd edition which had characters moving at 30' per 6 second round. However, using this slow, methodical rate allows for all the precautions that most adventurers are known for: checking for traps, watching all directions, careful mapping, etc. It also allows tall folk and smaller folk to move at roughly the same rate! However, I would state that this should not be the case, since if the smaller folk are also moving at a reduced rate, then they should be scaled with the humans accordingly. (Also note that Gygax only uses this slow rate for exploring unknown areas - when moving through mapped or known routes, the rate is 5x faster!)
One must remember that the better the armor, the slower the movement rate. A character in leather armor (non-bulky) is not restricted in movement rate, but one in chain mail (fairly bulky) is moving slower (9" base speed), and one in plate mail (bulky) is slowed even more (6" base speed). Human base speed is set at 12"; I've stated over the years that the smaller humanoids are shown to have a base speed of 9" while giants are shown to have a base speed of 15" or greater depending on size. Therefore, if a suit of armor reduces 12" to 9" or 6", this is a reduction of one or two 3" increments (one could argue for 3/4 or half instead). Since the armor chart in the DUNGEON MASTERS GUIDE (page 27) only deals with 3" increments, let's assume that this is the correct usage of movement reductions for armor. So, a halfling in plate mail is not moving at 4½" but rather at 3" (base speed of 9" reduced by two 3" increments). A human in plate mail is moving at 6", and this seems to make sense. It is not written into the rules anywhere, but still makes sense.
Now, let's take a look at page 28 in the DMG. Near the top of the page is a little section about magic armor. It reads as follows:
When magic armor is worn, assume that its properties allow movement at the next higher base rate and that weight is cut by 50%. There is no magical elfin chain mail.
This seems to work well with the base rate rules I've listed above! Accordingly, that halfling in magical plate mail can now move at the same rate as a human in normal plate mail, i.e. 6" base movement which is one 3" increment better than normal. Magic shields, on the other hand, have no bearing on movement and don't really cut weight, but are considered non-bulky.
Now here is where it gets confusing and contradictory. Normally, when the rules contradict themselves, it's because they were written at different times in different books (and possibly by different authors). However, this contradiction occurs within the confines of the same book and is likely written by the same author (dear old Mr. Gygax). If you look on page 164 of the DMG, under the section describing magic Armor and Shields (2nd paragraph), you find this little gem of a rule:
For game purposes all magical armor should be considered as being virtually weightless - equal to normal clothing, let us assume. This gives characters so clad a base movement speed equal to an unarmored man. Magic shields, however, weigh the same as a normal shield of the same size.
So, in the span of about 135 pages we've gone from "use the next higher movement rate" to "all magic armor is weightless." I really don't buy this - after all, players would argue that if their armor is weightless, they can go swimming in magic plate mail (which, I can assure you, is not the case according to any water-filled pit traps I've ever seen in any modules ever written). Why would the rule be changed so drastically from the beginning of the book to the end of the book? It's just one of those mysteries of the AD&D rules...
Now, in my campaign, this rule reared its ugly head and I had to address it head on. I opted to use the former rule regarding one 3" increment better, and the players agreed that it made more sense. Weightless armor should be reserved for elfin chain mail only, since this is the reason why elves are able to be fighter/magic-users and still wear armor (according to the original D&D rules, with a nod towards Tolkien's Lord of the Rings series). Now, do all fighter/magic-user elves have elfin chain? Probably not. So, should elven fighter/magic-users be able to cast spells in magical chain mail or plate mail? Again, probably not, but the multi-class rules seem to support this. On the other hand, if you are one of those DMs that removes the level limits for demi-human races, then perhaps you should consider enforcing a "no armor" policy for fighter/magic-users to make them less powerful. After all, if elves can run around casting spells in plate mail, you really can't expect the human magic-users not to be up in arms about not being able to wear some form of armor...
Later editions of D&D (notably 3rd and later) made it possible to wear armor and cast spells, but with a spell failure chance unless they were proficient in the armor that they wore (and there were three levels of armor proficiency - light, medium, and heavy). Perhaps, if spellcasters gave up a weapon proficiency slot to learn an armor spellcasting "proficiency" (say non-bulky, fairly bulky, and bulky) with a prerequisite of having the previous lighter proficiency before a heavier proficiency can be learned, this would allow fighter/magic-users to wear heavier armor and still cast spells without unbalancing the system (there must be a cost that limits the characters in some way). This would prevent low level magic-users from learning more than non-bulky armor proficiency OR a weapon, not both. It would also mean that 1st/1st level fighter/magic-user elves who want to wear plate mail can do so, but at the cost of 3 of their 4 starting proficiencies, leaving them proficient in only one weapon (or they can opt to spend 2 slots to get as high as casting in fairly bulky armor, and have 2 weapon proficiencies). I see this as more fair and provides more choice at the cost of reduced effectiveness. If a human magic-user wanted to wear armor using this system, he would have no weapon proficiencies at all, but could wear plate mail by the time he was 13th level, and would be able to learn his first weapon at 19th level! Not really a good idea for a magic-user with only 1 slot and additional slots every 6 levels! besides, one must determine if it's worth being armored if you have to fight when out of spells with nothing but a non-proficient weapon at -5 to hit! I would also require that characters have a minimum Strength score to wear such armor (say minimum of 9 Strength, same as for fighters).
Rangers, who also cast magic-user spells at higher levels, are not restricted in the armor that they can wear. But at 9th level, they are assumed to be wearing magic armor of some sort. Should they too be required to spend proficiency slots on spellcasting in armor? Perhaps casting in armor is not the issue, but instead casting in magic armor! If this was the direction that Gygax was leaning towards, it's possible that he really meant for all magic armor to be weightless after all! But why then restrict magic-users to wearing no armor, while allowing all other magic-user multi-classed characters to wear whatever armor they want? There doesn't seem to be an equitable answer. All thief multi-classed characters are restricted to wearing only leather armor while performing their thieving functions; why not restrict all arcane spellcasters to no armor if they intend to cast spells? There just doesn't seem to be a good reason for it!