Why practice punching in the air? Because it gives you the time to analyze what you’re doing without the excitement of impact.
Why practice on a focus pad and not a person? Because it removes the fear that you might hurt another person – it gives you freedom to go for it.
Why hit a person wearing a chest protector instead of just hitting someone for real? Because you can only do that so many times with out injury.
Why hit an actual person with a punch? Because that is, after all, the unfortunate situation we are training for. If we don’t know what it feels like then it may come as a surprise and we train to avoid surprises, to uncover them and to slowly come to an understanding of our actions and their consequences.