Translation:I will not eat animals that have a face.
A jelly fish or a star fish, for example.
Also, all invertebrates (butterflies, spiders) don't have a human-like face. And "tvář" is definitely a human-like face. And since most animals are invertebrates, we can say that most animals don't have a face (tvář). "Tvář mouchy" (the face of a fly) sounds silly, but I'm sure a few biologists would disagree with me.
Thanks - I was wracking my brains for animals without faces (not sure I'd be keen to eat jelly fish or spiders either personally!) - but it's also really interesting to learn that tvář has that particular connotation of a human-like face. It's the cheeks, I guess - which it also means, if I remember rightly.
Yes, "tvář" means "cheek" (singular) and it's also a nice word for a face. The normal word for a face is "obličej". Then there's also an ugly word for a face: "ksicht" or even "xicht", which is a German loanword.
Bugs technically have a face - basically just eyes and a mouth, plus antennae. We don't usually think about them having a face, but if we do, I guess the word "obličej" is usable just like "face" is in English, although biology simply talks about the head, eyes, etc., usually there's no need to explicitly say "face". But "tvář" is connoted with character and emotions, so using it even with birds or fish is stretching it.