I once got in an argument with someone who claimed a fish isn't an animal. And I laughed and said "of course it is. What else would it be a plant?". They said "It's not an animal. It's a fish!" So I said "which is an animal we can look it up if you want"
The reply I got was "I don't need to look it up I know a fish isn't an animal"
I got stunned into silence so I think in their mind they believe they were absolutely objectively proven correct. I don't put much worry in arguments since, easier to let things go and realise people are just stupid and ignorant.
I had this exact same argument with someone when he said he was a vegetarian. We were looking for a restaurant to eat with coworkers. Two sentences later he said he could eat fish, so I said "fish is meat, I thought you were vegetarian" expecting something about "it's just easier to say I am, but really I'm a pescatarian". But no. He said "fish is not meat"
I think people get "animals" confused with "mammals". Also there's some weird thing with Catholicism where fish isn't defined as meat for the purposes of Lent. But man it's infuriating to meet someone like that.
I got confused about this too, when I found out that traditionally meat has referred to warm-blooded animals. But that's not universal across cultures, "warm-blooded" has been an obsolete term for quite some time in biology, and thermoregulation is kind of a silly condition for something being considered vegetarian or not. A fish is clearly not a vegetable, unless in an induced coma, and I doubt they person only eats comatose fish.