Why does downsampling stretch a signals frequency response and upsampling shrink and create images of a signals frequency response?
I try to think of it this way: In the time domain, when downsampling occurs, the signal gets compressed; while on upsampling, the signal gets stretched. 

Then, from the Fourier transform we know that time stretching means frequency compression, and vice-versa.

It may not be a rigorous answer, but hope this helps!