I find the whole premise odd. Meat is fundamentally associated with living creatures. How could you have a concept of meat and simultaneously find it weird that creatures would be composed of it?
Obviously their conception of "biological matter" would then be much different and more general from our current conception of "biological matter", but what exactly in that difference makes ours inherently funnier than theirs?
There is an undercurrent here that drives the discussion. They know meat well enough not to like it, without knowing of any other thinking meat. So, they know of dumb animals, and animals eating other animals, and consider them disgusting to have around, for reasons obvious to one another, that we might not even be equipped to understand.
But we have exactly their reaction to outgroups of other people. So this is a lampoon of bigots who imagine themselves a cut above some other group. But they're just meat, too, and no more fit for galactic society.
And that is the fallacy.
I first heard the radio play (linked in another comment) and it took me a minute or so to realise they weren't humans and they were talking about us.