Taekwondo students over 16 ought to do Press ups on the Knuckles. This has a few benefits, which I'll cover further down. If knuckles are injured, you shouldn't do this though. It's particularly important that children do NOT do press ups this way as it can interfere with bone development and cause problems later in life.

It's vital that the press up is done on the first two knuckles (index and middle) and not on the "softer" ring and little finger knuckles. One of the reasons for doing press ups on the knuckles is to toughen them up so they make effective weapons, and won't let you down when you are asked to break a board or a brick at your grading or a demonstration.

However, I see the most important reason for doing this being that it "teaches" you to align your wrist correctly for punching. If a bent wrist is used to throw a punch, the wrist is likely to suffer a sprain or even a break. When you do press ups on the first two knuckles, you are forced to correctly align the bones of the fist, wrist and forearm into a straight line which is incredibly strong. Once you are using this straight line when punching, you will avoid injusry and maximise the effectiveness of your punches.