There's a term for people who don't eat meat, but eat fish:
Pescetarians.
I'd rather have it clear that people use the right terms, since some will probably complain about being given only vegetables when there was fish available, whilst happily claiming they are vegatarian.
it's almost like claiming that you are vegan when you are vegatarian.
I believe the reason is Catholicism. A sibling poster mentioned it being a thing in Poland as well (catholic), and I remember when I was a kid, on Fridays you would not eat meat, but fish was OK.
Having that tradition, that every Friday you don't eat meat, but fish is acceptable, seems to colour your perspective when thinking about what is being a vegetarian.
That's before Easter only, it is supposed to be about eating plainly. The 'no meat' thing is an historical residue, some fishes are actually more expensive than chicken, for example.
My teenage daughter's vegetarianism is about not knowingly eating cute animals - fishes are not cute enough for her. She'll happily eat meat-flavoured vegetables from dishes where cook and vegetables cook together. Whatever floats your boat - I'll respect that !
Here's the thing, in my opinion, that is the best attitude toward vegetarianism. One of the reasons we still slaughter so many animals, is that there is this misconception that for some reason, vegetarianism is an all or nothing type of thing.
If our culture were more akin to, `I don't like meat like I don't like candy`, animal consumption would drop considerably. Both candy and meat are tasteful, but candy is bad for your body and therefore you will not have it every day. The other is bad for the planet (and your body too!). Yet, you should for some reason either eat it every day, or alternatively never at all.
Try giving her a lobster in shell. I as an adult got the opportunity to try Maine lobster; never again. The whole process felt like dissecting someone who I'd rather play with.
Prepared correctly that situation could be quite the ethical connundrum. I find bacon alone to have a nonzero effect on 'reforming' vegetarians.
My personal rule is to avoid factory farmed meat. 100% effective when buying for home, but I admittedly compromise when eating out, but by asking each time I plant the seed I hope. I do, as an omnivore, think everyone should see, and take some part in, raising, and slaughtering livestock before it becomes a staple of your diet. Meat comes from animals that died for you, not the store. Respecting that has more impact than blanket-avoidance in my eyes.
In Poland it's not about vegetarianism (until recently, nobody cared about not eating animals), but about religious (catholic) traditions. From what I've heard, the logic for fish being allowed is, in Jesus time, meat was expensive, while fish was cheap. So, you fasted by abstaining from eating the fancy meat and only eating the pedestrian fish.