How can I explain lossless compression to a misguided audio engineer?

I have recently been involved in a discussion with someone who doesn't accept that lossless compression is possible, even in principle. This person considers himself to be technically literate, and an expert in his field of audio engineering.

I and several others have patiently tried to explain how lossless compression is possible, using simple examples such as run-length encoding and delta encoding, but he refuses to believe that it's possible for a lossless audio codec such as FLAC, for example, to exactly reproduce the input bitstream from the raw PCM data.

His response is always along the lines of:

it's getting smaller, so it must be losing data

"lossless" is just a buzzword used by software companies to sell their software, it doesn't actually mean lossless

Are there any other examples I can use to demonstrate conclusively that lossless compression is actually possible?

Tell him to write out the integers between 1 and 100, inclusive. Ask him how it can be that your instruction was so much shorter than the list of numbers he wrote out. Did that brevity cause him to write out the wrong thing?

StackExchange Computer Science Q#75859, answer score: 12