[maytc]

> Why can't we compress encrypted messages?

Not sure if eli5, but you can compress that message. Counter example: Huffman encoding that message.

[CodesInChaos]

You can't compress the ciphertext encrypted with typical encryption algorithms, because the output is indistinguishable from uniformly random bytes.

But you can losslessly compress data encrypted with Caesar encryption, because it's unbelievably weak.