It is a feature, as stated by Toady One:
03/17/2012 Toady One Damaged clothing that gets thrown out in the refuse pile will rot away now.
1) Armor is not "damaged clothing" and should have no means by which to ever BECOME damaged, thus Toady's quote above should never apply to this situation.
In other words, if it was truly the case that only "damaged clothing" rotted in refuse piles, that would not explain why armor rots in refuse piles, because how did the armor get damaged in the first place to qualify as "damaged clothing"? Thus, this is still a bug, if Toady intended the above quoted behavior, because that's not exactly what's happening.
What seems to actually be happening is "ALL clothing that gets thrown in a refuse pile, damaged or not, will rot now"
2) I'm pretty sure furniture and other stuff rots in a stockpile with refuse included, which also seems like a bug and is not implied by the above quoted feature. And even if this behavior is intended, at best it's absolutely horrible in terms of intuitive UI. If he wants to give you an option to make anything rot if you want it to in a stockpile (which we don't know that he does?), it should be a toggle option when you select any stockpile, down by the options to "link to buildings" etc. That way it would not happen by accident or overlap weirdly with other things you might want to do, like simply storing refuse and other things in the same stockpile -- especially likely for new players to do early in their very first forts making one big common stockpile.
Making new players' whole forts rot away unintuitively is not exactly a great feature to add to encourage more people to get hooked on the game.3) None of this explains why armor might be rotting while worn, which the OP explicitly confirmed is happening. Implying that the refuse flag carries over to things not even in refuse anymore or any stockpile, which is clearly a bug even if you don't think the other things are bugs.