When we make yes/no questions in English, we usually invert the subject and the auxiliary verb. The auxiliary verb and the subject change places. In the sentence:
The subject is he and the auxiliary is is. If we make a normal yes/no question, he and is change places like this:
Notice that we cannot move the words calling me. There is no special reason to move these words.
We have the same situation if we have a normal negative sentence:
Again, we can make a yes/no question. We can invert the subject he and the auxiliary is. We do not move the other words:
Notice that there is no special reason to move any of these words: not or calling or me. We don't have a special reason to move the word not in this example.
However, we can have a different version of the negative sentence. We can contract the auxiliary is and the negative word not. This gives us the contraction isn't:
This time, when we invert the subject and the auxiliary, the whole contraction isn't will invert with the subject. The auxiliary, is, will pull the n't section with it:
We can only move n't here because it is attached to is. The word not can only move to a new position because it is joined to is! If we do move it, it will sound very strange.
Hope this is helpful!
Why would we use Is he not calling me?
This question-form does not appear in the Original Poster's question. This form is likely to be used when the speaker expected that 'he' was going to call, but later finds out that he isn't. It is probably a 'checking' question. The speaker is checking that he isn't calling. Because of this, the speaker will give the word not contrastive stress. We can do this more emphatically if the word not is separated from the auxiliary.