Why Is Armor Only Available To Tanks?
MR itemization is open to more or less everybody. AD carries and AD casters have items like Maw of Malmortius and Mercurial Scimitar, AP carries have items like Abyssal Scepter and Athene's Unholy Grail, and with Locket and Banner, supports can buy MR for their whole team. Tanks have Banshee's Veil and Spirit Visage, among other options, obviously.
Armor, on the other hand, is much harder to come by: it's more or less only available for tanks. Dead Man's Plate, Frozen Heart, Randuin's Omen, Sunfire Cape, and Thornmail are all built almost exclusively by tanks. To the extent that Ohmwrecker and Zz'rot Portal are built at all, they're also tank items.
There are only a few exceptions: Zeke's is built exclusively by supports (and not so much anymore, since crit chance became so much easier to come by in the preseason patch). Iceborn Gauntlet is a tank item which can be built by Ezreal. The only actual carry item that gives armor is Zhonya's Hourglass, which is mandatory on most or all AP midlaners. If that's not cutting it, you have to go into a purely defensive tank item like Guardian Angel.
Why is this, though? ADCs, with their multiplicatively scaling damage, are meant to go after tanks, whose defenses also scale multiplicatively. If you're trying to encourage the ADCs to go out and bust tanks, why would you make it so that nobody else can build against them, making them far more effective against squishy targets? AP carries, with a few exceptions (Cassiopeia, Azir, etc.) perform poorly against tanks, since their linear scaling struggles to cope with tanks' defenses (HP counters magic damage as well as MR): if MR itemization followed the same logic as armor, tanks would only have one MR item.
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is most likely going to be changed in the mage update because right now it has an extreme case of confused identity. Once mages have a better anti-health item available I think we'll see sustained AP become more effective against tanks.
health+AD is a thing. I could be wrong here, but I think the fear is that AD+Armor becomes a must rush item in AD vs AD matchups, with the winner being determined by whomever got it first.