Methinks you might be confusing hurt with injure.
I learned the difference from a hockey coach when I was a kid. Paraphrased, every time you make contact, you do it with intent to hurt. You want him to feel it and to be sore from it. You hit him hard and he's going to be thinking about you next time you're on the ice with him. But never hit with intent to injure - that's a different thing all together.
And if you don't believe that 100% of NFL players target an opponent's hurt or sore arm, shoulder, wrist, etc, you may be incredibly naive.