This is what I think is the problem, and I am not having a go at you, it is just that when you say " I still have to classify myself as an ape" I see the Creationist type of logic, and no insulted intended in that. (I apologize).
You are an ape, but you did not 'become' an ape, your lineage, Homo sapien sapien, was once classified as something different, if you consider something other then Human, such as our closest Ancestors, Ape but not Us, it brings problems. We come into the problems of Definitions which are all, in this case, Arbitrary.
And are Homo sapien sapien really that different from our closest identified ancestor to get a new family name? A new definition? I know you do not think so. Personally, on a intellectual level, I feel and consider it good to make people understand our heritage, that we are not only Apes but our family History is amazing and think that telling children or generally defining us as 'Unique' (in an arrogant way) is negative and even if you do not do this (I understand your point perfectly) I think that it is a path that would eventually damage our soceity because we would, just as Patriots/Nazis/Nationalists makes people biased and prone to accept lies and falsehoods.
I hope you can see my point.