I think it’s still useful to have informal words that distinguish smaller, typically less intelligent primates from larger and typically smarter ones, but I agree that using it as a gotcha is pointless.

It’s like people using the botanical distinction about berries, legumes, etc to argue that some savory plant part isn’t a vegetable (e.g. tomatoes as fruits, bananas as berries, etc). What’s scientifically correct comes second to clear mutual communication, and no one likes a smart-ass.

Besides, we as mammals are really just all confused fish.