Short Answers

Yes, I am.
vs 
Yes, I’m.


"Wow! but why?", asked my students. 

Good question. The thing is that we need to explain more than just two different ways of writing short answers in English. It's not only like he's and he is, and that's it. There's much more inside the English language. Emphasis is for the long answers and intonation plays an important role in the meaning of words too.

So, as you can see, this story is not so simple: when you respond to someone with a short answer, you normally confirm what you've just been asked about, and for that reason, you need the long answer here (Yes, I am / He is), in order to assert your response or make it clear.

I hope this is not very complicated for you. Anyway, you can always have a look at this Wordreference Forum about the same topic, and more advanced theory on emphasis.