Differences between downsampling and upsampling
That is because downsampling aliases the spectrum, while upsampling duplicates it. As an example, consider a sampled, single-tone signal:

The DFT of this signal has a single tone, as expected.

If we downsample by throwing away every other sample, we would alias any high frequency content but since there isn't any we still have a single tone.


When we upsample, we add samples in-between each existing sample. We have to add these samples with a value of '0' since the upsampling processes doesn't know the original signal.

The upsampled spectrum is duplicated and now has two tones. The magnitude of each tone is reduced by 1/2 but the total power of the DFT is the same.

If we re-downsample this signal by throwing away every other sample (the '0's we added) then the high-frequency tone would alias to a lower frequency and the magnitude of the lower frequency tone would increase. For more detailed analysis, check out Parseval's Theorem.
How you determine the best value of the '0' valued samples added during upsampling is the job of the interpolation filter. A good video discussing this for digital audio is on xiph.org.