Why does downsampling stretch a signals frequency response and upsampling shrink and create images of a signals frequency response? I am learning some basic DSP and I have a pretty good intuition as to why sampling creates spectral images of the frequency response at intervals of the sampling frequency (convolution with pulse train).

I am reading about sample rate conversions (downsampling/decimation and upsampling/interpolation) and I can't seem to get intuition as to why downsampling/decimation stretches the frequency response by M (the downsample factor) or why upsampling/interpolation compresses it by I (the upsample factor) and creates more images of the originally sampled datas 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!