Good one.  But I would say that it could have been made anywhere.  I'd start by looking at the various bio-warfare labs scattered about.

I absolutely would not put it past the Chinese govt to develop and deploy such a thing against their number one enemy (their domestic population) if it served some useful purpose or if they were directed to do so by their controllers (e.g., as a trade for having moved capital there over the last few decades.)

At the same time I would not put it past quasi-adversaries in the West to deploy the goodie in Wuhan as a starting point.

One way or another, it won't stay a Chinese problem for long so where it started doesn't really mean a lot.  One operative with some liquid could start it wherever they so choose and could have it pop up anywhere else which was advantageous.

Could it be from the gooks eating bats?  Sure it could.  But that psy-op being spread around social media lends exactly zero support to the hypothesis.  As a matter of fact depending on how social media was used to spread the idea (which I've not researched) it could be that the fact it spread via social media might be taken to strongly indicate that the story is a flat-out lie.

We'll know more as time goes by.  At those of us who expand our foraging range to outside of the mainstream media will.