In some Buddhist countries (like Japan and Sri Lanka), the vegetarian ideal allowed fish to be part of the diet, at least for laypeople.
There are debates involving the fact that, since fish aren’t warm-blooded like chickens or goats or cows, their flesh wasn’t really “Meat”. Since Non-vegetarianism involves eating “meat”, eating Fish could still be considered Vegetarianism.
But the glitch in theory still remains that fish have eyes and parents, and are living creatures, so eating them would not be considered Vegetarian. This is why a new category was created for those who wished to incorporate fish into their vegetarian diets - these people were called Pescatarians.
But the term "Pescatarians" is not that well known and often goes overlooked. International Airlines find it extremely confusing when asked for Vegetarian meals because most of them don’t consider lean meat (chicken, fish) and eggs to be Non-vegetarian. So if you ask for an Oriental Veg meal on ‘AirChina’, you will surely be served fish.
But in all logic and common sense, it remains that Fish cannot be considered vegetarians and the places that do so, should stop. It is torturous for a vegetarian to have to see/smell fish on their plate. It’s like, if you ordered for Dairy Milk, but you were served dung.
Now, to all the fish lovers- I’m not saying Fish is equivalent to ‘dung’. Imagining it to be so is just a way to understand the point of view of vegetarians who have to constantly listen to “FUUCK! You’re a Vegetarian? You don’t even eat egg? Have you ever tried meat it by mistake?”. Vegetarianism is a lifestyle, just let the people be. Don’t scare them with articles with confusing titles that make it seem like ‘Fish’ might be vegetarian after all.