Here's the thing. You said a "mountain lion is a lion." Is it in the same family? Yes. No one's arguing that. As someone who is a scientist who studies lions, I am telling you, specifically, in science, no one calls mountain lions "lions". If you want to be "specific" like you said, then you shouldn't either. They're not the same thing. If you're saying lion family" you're referring to the taxonomic grouping of Felidae, which includes things from house cats to ocelots to tigers. So your reasoning for calling a mountain lion a lion is because random people "call the big ones lions?" Let's get panthers and leopards in there, then, too. Also, calling someone a human or an ape? It's not one or the other, that's not how taxonomy works. They're both. A mountain lion is a mountain lion and a member of the lion family. But that's not what you said. You said a mountain lion is a lion, which is not true unless you're okay with calling all members of the lion family lions, which means you'd call house cats, tigers, and other cats lions, too. Which you said you don't. It's okay to just admit you're wrong, you know?