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Here's the thing. You said "Ultra Beasts are Legendaries."
Is it in the same family? Yes. No one's arguing that.
As someone who is a scientist who studies legendaries, I am telling you, specifically, in science, no one calls ultra beasts legendaries. If you want to be "specific" like you said, then you shouldn't either. They're not the same thing.
If you're saying "legendary family" you're referring to the taxonomic group of Legends, which includes things from Mewtwo to Phione to Jirachi.
So your reasoning for calling ultra beasts legendaries is because random people "call the black ones legendaries?" Let's get Unown and Mega Charizard X in there, then, too.
Also, calling someone a human or an infernape? It's not one or the other, that's not how taxonomy works. They're both. An ultra beast is an ultra beast and a member of the legendary family. But that's not what you said. You said an ultra beast is a legendary, which is not true unless you're okay with calling all members of the legendary family legendaries, which means you'd call Shaymin, Jirachi, and other mythicals legendaries, too. Which you said you don't.
It's okay to just admit you're wrong, you know?