In case you're unaware, the "deep inhale" is because that phrasing is historically tied to the WINE project, as per their website (winehq.org):

Wine (originally an acronym for "Wine Is Not an Emulator")

And at this point it's like a 10-year old meme (if not 20) to bring it up when someone may seem unaware of the distinction between emulation and what Wine does.

It is a bit tired of a reference, and I imagine somewhat off-putting of a response to receive when you don't know the reference yourself. The acronym is in the spirit of the GNU one ("GNU's Not Unix"), and as the other commenters have explained the fact that wine does something different than emulation is very relevant when you get into the nitty-gritty details, so it has extra sticking power in terms of memes in linux/foss communities.