The way I imagine the armor-piercing bonus to make it seem logical is this:

I could run circles around a man in full-plate-mail armor. I could run around behind him and push him over. Aside from wildly swinging his sword, I dont think he'd have much chance to stop me. Once he's down I can pry up his helmet and stab him in the neck. Boom. He's out.

(Correct me if I'm wrong) Heavy armor developed to protect the wearer from ranged attacks--arrows and later musketballs. It was particularly useful for mounted knights who had to run headfirst into a hail of arrows, and had all the maneuverability they needed as long as they stayed on their horse.

Infantry in anything other than chainmail (armor 3?) is going to get outmaneuvered by lightly armored troops. If those troops are skilled at attacking an armored unit (i.e. "armor piercing") they should be able to make use of their manueverability advantage in the form of a bonus.

At least that is one way to "justify" the somewhat whacky armor system.